Aplusclick Thinking Outside The Box Questions




ID 9009

Think Outside The Box The first four Volumes of the Delicious Food Encyclopedia are stacked vertically side by side on a shelf. There 400 pages in each Volume.

A well-educated worm ate paper in a hole from the first page of the First Volume to the last page of the Fourth Volume.

How many pages did she taste?



ID 9022

Think Outside The Box Gerry and Jane play a game.
A player must take off one or two neighboring petals when it is their turn.
The winner is the player who takes the last petal.

Gerry starts first.

Can you guess the winning strategy for one of them?

If YES, who wins?



ID 9024

Think Outside The Box We construct a building 7 km wide, 7 km long, and 7 km high.
The passages and lifts are 20% of the building volume.

If a person receives a cubical apartment 3 meters wide, 3 meters long, and 3 meters tall, what is the largest population that could live in the building?

1 km = 1,000 meters



ID 9040

Think Outside The Box A magician tells you that if you correctly guess the exact value of money in an envelope then he will give you the money.

The envelope contains bills (notes) totaling between $1 and $9 (inclusive). After each guess he will tell you if your guess is too high or too low, or he will give you the money in the envelope. You can try only 3 times.

What is the expected amount of the money for you?



ID 9066

Think Outside The Box A barber wants to write the word COOL on a board behind the client’s seat in such a way that a client looking in the mirror reads the word correctly.

Which of the following should the barber write on the board?



ID 9068

Think Outside The Box Which diagram cannot be drawn without lifting your pencil off the page and without drawing along the same line twice?



ID 9069

Think Outside The Box Seven pirates share 77 gold coins that were arranged in a line.
The first pirate takes every seventh coin,
the second pirate takes every sixth coin,
the third pirate takes every fifth coin,
. . .
the seventh pirate takes all the rest.

Who gets more coins?



ID 9073

Think Outside The Box Twins Ron and Roy and their humanoid robot Rob go for a walk in the Sahara. Rob looks like the brothers.
Ron can run at 20 km/h in the desert, Rob 5 km/h slower, and Roy never tried.

Suddenly, they see a lion at a distance of 300 meters, who is the desert sprint champion with the record speed of 30 km/h at a distance of 1 km.

What is the smallest safe speed for Roy to run to their car that is at a distance of 600 meters?



ID 9104

Think Outside The Box Five remote research stations need to share their research data with all the other stations. Sadly, due to cost cutting at the design phase, the high bandwidth bi-directional data links all route through a central hub, so only two stations can share data at a time. The data sharing time is independent of the amount of data shared, but the switching time is huge. In total each transfer takes 1 minute.

What is the minimum amount of time required to fully share the data?



ID 9177

Think Outside The Box There are 100 lockers in a school. Gerry opens every single locker. Then he closes every second locker. Then he goes to every third locker, closing it if it is open, or opening it if it is closed. Then he does the same with every fourth locker and so on. The process is completed with the hundredth locker.

How many lockers are open at the end?



ID 9178

Think Outside The Box A question at a job interview.

 A bathtub is ¾ full of water.
You have a teaspoon, a teacup, and a bucket.

What would you use to empty the bathtub?



ID 9222

Think Outside The Box Alice is a well-educated, law-abiding girl. She goes to her school.

Can you guess the country where she lives?



ID 9244

Think Outside The Box Assign the numbers 1, 2, 3, 4, 5, 6, 7, and 8, placing one number at each corner, such that the sum of the four numbers on each side is the same for all six sides.

What is the sum?



ID 9250

Think Outside The Box A king travels at a speed of 8 km/h from his castle to a battle. Each four hours he sends a messenger with a speed twice as fast as the king back to the castle.

How often does the queen in the castle receive the messages?



ID 9253

Think Outside The Box A group of 8 people go to a fishing trip.
There are 2 boys among them.

What is the maximum possible number of people who have sons in the group?



ID 9331

Think Outside The Box A seller told me by phone that "Any number from 1 to 9 costs $209, from 10 to 99 costs $218, and so on."

Please tell me how much 100 costs.



ID 9338

Think Outside The Box Please use five numbers 1, 2, 3, 4, 5, and all these signs. Parenthesis and power are not allowed.

What is the largest possible result of your expression?



ID 9389

Think Outside The Box If ⅔ of SMALL is equal to ¼ of BIG, how many times is BIG greater than SMALL?



ID 9399

Think Outside The Box Please find the last number.

3 → 0
4 → 2
5 → 5
6 → 9
7 → ?

Hint : the MENSA question is linked to geometry.



ID 9412

Think Outside The Box A fast-growing pond-lily doubled the pond area it covered every day, so that by the end of the twelfth day it had covered the entire pond.

Another pond of similar size is available, and instead of planting one lily we plant 4, appropriately spaced. Assuming they all grow at the same rate, how long will it take to cover this new pond?

(Keep it simple: only consider the area covered and not the shape.)



ID 9420

Think Outside The Box What is the value of

cos 0° + cos 1° + cos 2° + … + cos 359° + cos 360°?



ID 9423

Think Outside The Box I take the smallest number on a telephone's number pad, then either add or subtract the next number, then repeat the procedure until all the numbers are used.

What is the most probable result?



ID 9492

Think Outside The Box The ball's design stitches together hexagons with pentagons. The ball made its World Cup debut as Adidas' Telstar in 1970 in Mexico. The ball's pattern of white hexagons with black pentagons made it easily visible on television.

If there are 32 hexagons and pentagons, how many pentagons are there?



ID 9495

Think Outside The Box Gerry uses L-shaped tiles to cover the 5 x 8 rectangle.

Certain tiles are not like the majority of the tiles.

How many tiles are odd?



ID 9501

Think Outside The Box On the 6x6 grid, we color a square in blue and continue with the neighbor square, so that each colored square has a common side only with one or two other colored squares. For example, we colored 20 squares.

What is the maximum possible number of such colored squares on a 6x6 grid?



ID 9503

Think Outside The Box I planted six apple trees in my garden, and then several pear trees, so that there are always two pear trees at a distance of exactly six meters from each of the six apple trees.

What is the minimum possible number of the pear trees?



ID 9532

Think Outside The Box When is it safe to jump out of an airplane without a parachute?




ID 252

Think Outside The Box How many letters are there in the correct answer to this question?



ID 406

Think Outside The Box The number of hours left today is half of the number of hours already passed.

What time is it?



ID 476

Think Outside The Box Brad has as many brothers as sisters.

How many more brothers than sisters does his sister Sue have?



ID 555

Think Outside The Box If you write all numbers from 0 to 109, which digit (numeral) will you write most often?



ID 649

Think Outside The Box The product of three consecutive whole numbers is 999,900.

What is the smallest of the three numbers?



ID 672

Think Outside The Box Four friends tried to guess the number of sheep in a flock.

Alex guessed 21,
Bob guessed 26,
Chris guessed 20, and
Daniel guessed 21.
Two were wrong by 2, and two were wrong by 3.

How many sheep were in the flock?



ID 729

Think Outside The Box Alex needs six tacks to fix two rectangular pictures because he can overlap the pictures.

What is the least number of tacks he needs to tack eleven pictures?



ID 740

Think Outside The Box Five students put their sandwiches into five paper bags. The bags are randomly distributed to the students.

What is the probability that all the five students receive the correct bag?



ID 825

Think Outside The Box Fifteen numbers have an average of 15.
Five of these numbers have an average of 5, four other numbers have an average of 4, three an average of 3, and two an average of 2.
What is the remaining number?



ID 865

Think Outside The Box Anna's income is seven-eighths that of Beatrice. Anna's expenses are seven-eighths those of Beatrice.
The girls' expenses are less than they earn.

Given that the girls save all that remains from their earnings after their expenses are paid, who saves more?



ID 886

Think Outside The Box How many times do the hour and the minute hands form a 90-degree angle in the course of 12 hours?



ID 895

Think Outside The Box The last digit of the number 333 is:



ID 898

Think Outside The Box How many planes of symmetry does a cube have?



ID 908

Think Outside The Box The number 99! is very big.

How many zeros are there at the end of the number?



ID 972

Think Outside The Box I roll two dice.

What is the probability that the second number is greater than the first?



ID 974

Think Outside The Box What is the maximum number of squares you can make using twelve identical matches?

You cannot cut the matches.
(The matches must not cross each other.)



ID 1036

Think Outside The Box The product of 2 integers is 1000.

Find the smallest possible sum of these numbers.



ID 1055

Think Outside The Box A lady, attempting to avoid revealing her real age to her husband, says:
I'm twenty-two years old if you do not count weekends and one summer month of every year.

Guess her real age.



ID 1061

Think Outside The Box It costs $24 to paint a cube, the cost being proportional to the surface area.
Before painting, it was cut in two pieces by a plane.

What is maximum possible cost to paint these two pieces?



ID 1124

Think Outside The Box What is the smallest integer that is 4 times the sum of its digits?



ID 1350

Think Outside The Box What is the units digit of 1! + 2! + 3! + ... + 2011!?

4! means 1 x 2 x 3 x 4



ID 1355

Think Outside The Box There are four brothers in a family.
The sums of the ages of three of them are 30, 32, 32 and 35.

What is the age of the eldest brother?



ID 1372

Think Outside The Box The left picture shows nine dots arranged in a 3 x 3 square.
The dots are connected using only four straight lines and without lifting the pen from the paper.

The right picture shows seven dots evenly distributed on a circle and a dot in the center.

How many straight lines connect the dots in the same way?



ID 1394

Think Outside The Box Two princes and two princesses are ready to marry.
Everybody independently chooses a partner without telling anyone.

What is the probability that at least one princess chooses a prince that chooses her?

Assuming that boys choose girls and girls choose boys.



ID 1462

Think Outside The Box The picture shows a tiling pattern which is made of square green tiles 10 x 10 cm and gray tiles 20 x 10 cm.
The pattern is extended to cover a large surface.

What fraction of the surface is colored green?

( A part of the pattern that is regularly repeated is smaller than the shown set of tiles.)



ID 1469

Think Outside The Box I wrote all the numbers from 0 to 999.

Which digit did I write less than the others?



ID 1479

Think Outside The Box The diagram shows 15 billiard balls that fit exactly inside a triangular rack.
The rigid rack prevents the balls from sliding.

What is the largest number of balls that can be removed so that the remaining balls are theoretically unable to move?



ID 1605

Think Outside The Box There are 10 girls and 10 boys in a class.

A teacher randomly chooses two students.

What is the probability that they are a boy and a girl?



ID 1616

Think Outside The Box Multiply all positive two-digit numbers.

How many zeros are there at the end of the result?



ID 1629

Think Outside The Box You have four piles: three piles with real coins and one pile with fake coins.
All the real coins weigh 20 grams each, and the fake coins weigh 21 grams.

How many times do you need to use a digital kitchen scale to find the pile with the fake coins?



ID 1658

Think Outside The Box Benny Bunny starts jumping from a hole.
Every leap is two times longer than the previous one.
Does Benny have a chance to come back to the hole?



ID 1670

Think Outside The Box How many times do the two hands of a clock point in the same direction between 9:00 am and 9:00 pm ?



ID 1671

Think Outside The Box After a gun is fired in a saloon, 75% of the cowboys have a wounded ear, 80% have a wounded eye, 85% have a wounded arm, and 90% have a wounded leg.

What is the smallest percentage possible of cowboys who have all four wounds?



ID 1675

Think Outside The Box It takes 2 cards to build 1 floor of a card house.
It takes 7 cards to build 2 floors of a card house.
It takes 15 cards to build 3 floors of a card house.

How many cards does it take to build a 10-story house?



ID 1698

Think Outside The Box I must balance any whole number load from 1kg to 40kg using these four weights and a balance.

What is the largest weight?



ID 1778

Think Outside The Box Based on 20 years per generation, estimate the number of ancestors John has in 200 years, if none of them appears more than once in the list.



ID 1820

Think Outside The Box What is the sum of all the digits (not numbers) in the sequence 1, 2, 3, 4, . . . 98, 99?



ID 1826

Think Outside The Box Two dice are thrown.
Two numbers are multiplied.

What product of numbers is most likely to occur?



ID 1828

Think Outside The Box Two cards are randomly chosen.
Two numbers are added.

What sum of numbers is most likely to occur?



ID 1829

Think Outside The Box What is the average of the smaller of two random numbers from 0 to 1?



ID 1830

Think Outside The Box What is the average of the smaller of three random numbers from 0 to 1?



ID 1831

Think Outside The Box Three white hens and four black hens lay as many eggs in five days as two white hens and four black hens lay in six days.

Which color hen lays the greatest number of eggs?



ID 1833

Think Outside The Box A kitten has a 50/50 chance to be male or female.
My cat just delivered two adorable kittens.
My veterinarian said that at least one of them is female.

What is the probability that the other kitten is a boy?



ID 1886

Think Outside The Box Bob the plumber has 10 pockets and 60 nuts.

He wants to put the nuts in all of his pockets so that no two pockets have the same number of nuts.

What is the largest number of nuts that a pocket can possess?



ID 1941

Think Outside The Box How many three-digit numbers containing only even digits are divisible by 9?



ID 1944

Think Outside The Box What is the largest digit in the product of 11111111 x 11111111 ?



ID 1949

Think Outside The Box What is the maximum number of pieces that an apple can be divided into with four straight planar cuts?

The pieces do not move.



ID 1952

Think Outside The Box What is the smallest positive integer that has 12 different positive divisors, including 1 and itself?



ID 1973

Think Outside The Box What is the largest product of positive integers that add up to 17?



ID 1975

Think Outside The Box What is the sum of all 5-digit integers which each use all of the five digits 1, 2, 3, 4, and 5?



ID 1989

Think Outside The Box What is the probability that a point chosen randomly from the interior of an equilateral triangle is closer to a vertex of the triangle than it is to a midpoint of one of the triangle's sides?



ID 2025

Think Outside The Box A farmer puts several pigs into three pens.
None of the pens is empty.
All pens contain different even numbers of pigs.

What is the smallest number of pigs?



ID 2027

Think Outside The Box How old is the eldest of these four sisters if the product of their ages is 792?



ID 2033

Think Outside The Box San Jose Scrabble® Club No. 21 published a three-letter word list that included 1014 English words.

Estimate the percentage of these words compared with all possible three-letter combinations?



ID 2051

Think Outside The Box Three apples were weighed in pairs and the weights were 200, 204, and 208 grams.

What is the weight of the lightest apple?



ID 2063

Think Outside The Box Thinking outside the box:

52 - 28 = 4

Which digit has to be moved to make the equation correct?



ID 2079

Think Outside The Box This shape was formed by removing a small cube from a big cube.
The side length of the removed cube is two thirds of the side length of the original cube.

What is the volume of the new shape compared with the original volume?



ID 2152

Think Outside The Box In the city of Konigsberg there were seven bridges.
There was a tradition to walk and cross over each of the seven bridges.
If a young man starts and finishes at the same point, what is the smallest number of crossings he would have to make?



ID 2157

Think Outside The Box In a city, there were seven bridges.
There was a tradition to walk and cross over each of the seven bridges.

If a person starts and finishes at the same point, what is the smallest number of crossings the person would have to make?



ID 2158

Think Outside The Box Four matchsticks form a square.

How many non-overlapping squares can be formed using eight matchsticks?

Note: The matchsticks do not intersect each other.



ID 2177

Think Outside The Box Three mentors and four apprentices produce as many devices in five days as two mentors and four apprentices do in six days.

Who is the best performer?



ID 2186

Think Outside The Box Guesstimation.

How many tennis balls can fit in a school bus?



ID 2188

Think Outside The Box What is the maximum number of apples (ideal spherical units) that can touch another given apple (spherical unit) without overlapping?



ID 2190

Think Outside The Box How many different cubes can I make by using six different colors such that each face has a different color?

I can rotate the cubes.



ID 2191

Think Outside The Box There is a legend that a stork brings babies to a village.
All parents continue to have children until they have a boy.
If they have a girl, then they try to have another child.
They stop if they have a boy.
The probability of giving birth to a boy is 50%.
What is the proportion of boys to girls in the vilage?

The photograph courtesy of Roland Sauter



ID 2193

Think Outside The Box A sphere fits inside a cube. The maximum possible ratio of the volume of the sphere to that of the cube is pi / 6, or about 0.52.

If we put many small spheres inside a cube, then what is the largest possible ratio of the spheres' volume to that of the cube?



ID 2195

Think Outside The Box I want to measure exactly six minutes from the moment I touch an hourglass, using only a five-minute hourglass and a four-minute hourglass.

How many times do I flip over an hourglass?

Count the initial flip(s) and find the minimum possible number.



ID 2198

Think Outside The Box I want to cut a wooden cube that is five inches on each side into 125 one-inch cubes.

I can do this by making 4 + 4 + 4 = 12 cuts, keeping the pieces together in the cube shape.

What is the minimum number of cuts needed if rearrangement of the pieces after each cut is allowed?



ID 2200

Think Outside The Box I arranged twelve one-inch wooden sticks in a polygon with an area of 6 square inches.
I would like to form a polygon with an area of 4 square inches using these 12 sticks.

What is the minimum number of sides of the new polygon?



ID 2204

Think Outside The Box You have 240 golden bricks identical in size and appearance but one is lighter than the others.

How many times do you use a balance scale to find the odd brick?



ID 2205

Think Outside The Box Logic puzzle: a secret door.

A man approached the door of a secret laboratory and the door robot said "SIX." The man replied, "THREE" and was let in.

Another day, the robot said, "TWELVE."
The man replied, "SIX" and was let in.

Today, the robot said, "FOURTEEN."

What should the man say?



ID 2207

Think Outside The Box The difference between a two-digit number and the two-digit number obtained by interchanging the positions of its digits is 72.

What is the sum of the two digits of that number?



ID 2208

Think Outside The Box Find the angle between two diagonals drawn on two faces of the cube.



ID 2209

Think Outside The Box I have four boxes, each containing identically shaped balls: one of them is black.
A ball is randomly drawn out of each box.

What is the probability that at least one of the four balls is black?



ID 2211

Think Outside The Box In a bakery store, 400 customers participated in a survey on Tuesday.
On Wednesday, 500 customers were asked at random, of which 40 confirmed that they were surveyed the day before.

Estimate the number of customers per day in the store.



ID 2213

Think Outside The Box An entrepreneur wants to hire the best person for a position.
He makes a decision immediately after the interview.
Once rejected, an applicant cannot be recalled.
He interviews N randomly chosen people out of 100 applicants, rejects them and records the best score S.
After that, he continues to interview others and stops when the person has a score better than S.

What number N do you recommend to the cruel man?



ID 2216

Think Outside The Box Logic riddle

In a house, there are three switches on the ground floor for three light bulbs in the cellar. I cannot see the lights from the ground floor.

What is the minimum number of trips to the cellar I need to make to identify which switch corresponds to which light bulb?



ID 2225

Think Outside The Box How many three-digit numbers have exactly five divisors including 1 and itself?



ID 2227

Think Outside The Box One hundred soldiers form a 10 x 10 square.

From every column, the tallest soldier is chosen, and from these 10 soldiers, the shortest is chosen. His height is X.

At the same time, the shortest soldier is chosen from every row, and from these 10 soldiers, the tallest is chosen. His height is Y.

Compare the heights.



ID 2230

Think Outside The Box There are 9 children in a class and each knows a different piece of a short story. They are allowed to exchange what they know via email.

What is the minimum number of emails required to enable each child to know the whole story?



ID 2232

Think Outside The Box Find the odd one out.



ID 2233

Think Outside The Box On average there are 100,000 strands of hair on a person's head.
Hair grows at a rate of about 15cm a year and each hair lasts up to 6 years before it falls out.

If the population of London is 8,000,000, what is the probability that at least 2 of the inhabitants have the same number of hairs on their heads, discounting bald people?



ID 2234

Think Outside The Box What is the next letter in this series?



ID 2235

Think Outside The Box What is the largeest number of matchsticks I need to remove to make 10?



ID 2237

Think Outside The Box You are shrunk so that your height is equal to the diameter of a dime (a ten-cent coin) and your mass is proportionally reduced so as to maintain your original density.

Who is heavier, you or the dime?



ID 2239

Think Outside The Box I have a rectangular piece of cheese with a round hole.
What line cuts the piece of cheese into two parts of equal weight?



ID 2241

Think Outside The Box A donkey must transport 900 carrots to the market, which is 300 miles away.
The donkey carries a maximum of 300 carrots, and eats 1 carrot every mile.

What is the largest number of carrots that can be delivered at the market?



ID 2242

Think Outside The Box Make two fractions with all the digits from 0 to 9.
Use each digit once.
They add up to exactly 1.

What is one of the fractions?



ID 2244

Think Outside The Box It takes exactly 1 hour to burn a rope when I light one of its ends.
The rate of burning is completely random, but the final result is always 1 hour.

How many different periods of time can I measure with 2 such ropes?



ID 2245

Think Outside The Box I place 1000 coins in two columns in a wooden box, and they fit nicely as shown.

How many more coins can I place into the box if its width is increased by 30%?



ID 3584

Think Outside The Box What is the average of the largest of N random numbers from 0 to 1?



ID 3587

Think Outside The Box Logic riddle:

In a house, there are three switches on the ground floor and a light bulb in the cellar. I cannot see the light from the ground floor.

What is the minimum number of trips to the cellar I need to make to identify which switch corresponds to the light bulb?

We assume that the bulb in the cellar works, that there is power to the house, and that one of these three switches will switch on the cellar light.



ID 3640

Think Outside The Box Benny Bunny starts jumping from a hole.
It takes six seconds for every 10 jumps. How much time does it take him to do 45 jumps?



ID 3662

Think Outside The Box Six goldfish need 2/3 of a cup of fish food per week.
How many fish could be fed with three cups?



ID 3685

Think Outside The Box Which city is the odd one out?



ID 3692

Think Outside The Box What word has letters that are not in alphabetical order?



ID 3694

Think Outside The Box Is it legal for a man in Montana to dance with his widow's sister at her marriage ceremony?



ID 3707

Think Outside The Box If you rearrange the letters NAMELESS, you would have the name of a



ID 3711

Think Outside The Box Logic puzzle.

Only the first and last letters of the words below are in their correct places.
The other letters have changed places.

Guess the answer.

Stenvey-ehigt muins stixy-terhe is



ID 3712

Think Outside The Box A pyramid and a tetrahedron with edges of the same length are glued together on a triangular face.

How many faces does the resulting solid have?



ID 3713

Think Outside The Box "Three sailors come across a pile of coconuts. The first sailor takes half of them plus half a coconut. The second sailor takes half of what is left, plus half a coconut. The third sailor also takes half of what remains, plus half a coconut. Left over is exactly one coconut, which they toss to a monkey.

How many coconuts were in the original pile?"

Martin Gardner



ID 3714

Think Outside The Box I take half of the coconuts plus a coconut.

What percentage of coconuts do I have?



ID 3717

Think Outside The Box I want to measure exactly six minutes using only a five-minute hourglass and a four-minute hourglass.

How many times do I flip over an hourglass?

Count the initial flip(s) and find the minimum possible number.



ID 3718

Think Outside The Box I need 1 + 9 + 25 = 35 cubes to build a pyramid with a height of 3 cubes.

Estimate the number of cubes for a pyramid with a height of 30 cubes.



ID 3719

Think Outside The Box If you wrote all the whole numbers from 1 through 1000, how many times would you write the digit 4?



ID 3727

Think Outside The Box Mount Everest is the Earth's highest mountain with a peak at 8,848 meters (29,029 ft) above sea level.
Indian mathematician Radhanath Sikdar was the first to identify Everest as the world's highest peak in 1852. Edmund Hillary and Tenzing Norgay reached the summit on 29 May 1953.

What was the highest mountain in the world before Mount Everest was discovered?



ID 3730

Think Outside The Box If you rearrange the letters NAPDOL, you would have the name of a



ID 3732

Think Outside The Box If a square is four and a triangle is three, how many is a regular star?



ID 3737

Think Outside The Box I place 11 chairs along the walls in an empty rectangular room.
The number of chairs along each wall is the same.

Find the number.



ID 3744

Think Outside The Box The Lucas problem.

François Édouard Anatole Lucas (1842-1891) was a French mathematician.

Every day at noon, a ship leaves Le Havre for New York and another ship leaves New York for Le Havre. The trip lasts 7 days and 7 nights.

How many ships will a ship leaving Le Havre today meet at sea?



ID 3749

Think Outside The Box A man eats 20 coconuts in 20 days. Together with his wife, they eat the same amount in 12 days.

How many days does it take the wife to eat this amount by herself?



ID 3750

Think Outside The Box There are 12 people in a village.
They consume 12 coconuts altogether.
Each man eats two coconuts, each woman eats a half, and each child eats a quarter.

How many men are there?



ID 3753

Think Outside The Box Vladimir Arnold (1937-2010), one of the greatest 20th century Russian mathematicians told the following story:

“Our schoolteacher, I. V. Morozkin, gave us the following problem:

Two old women started at sunrise and each walked at a constant (different) velocity. One went from A to B and the other from B to A. They met at noon and, continuing with no stop, arrived respectively at B at 4 p.m. and at A at 9 p.m.

At what time was the sunrise on this day?"



ID 3754

Think Outside The Box Inspired by Morozkin's problem :

Two children started at 6:00 and each walked at a constant (different) speed.
A boy went from A to B and a girl from B to A. They met at noon and continued with no stops. The boy arrived at B at 4 p.m.

At what time did the girl arrive at A?



ID 3756

Think Outside The Box 1 gives 2
2 gives 6
3 gives 12
4 gives 20

What does 10 give?



ID 3758

Think Outside The Box A committee consists of 7 people. The committee keeps an important object in a safe.

How many mechanical locks must the safe have so that it can be opened precisely when at least 4 members of the committee are present?

You may suggest your design of the lock(s).



ID 3772

Think Outside The Box Guesstimation

A man can jump up to four times the length of his own body.
Frogs can jump up to fifty times their length.
A flea can jump 350 times the length of its own body.

What is the average length of these three jumps?



ID 3807

Think Outside The Box Thinking outside the box:

Which statement is correct?



ID 3889

Think Outside The Box Job interview logic puzzle in a bank.

Which of these pieces of information would be most useful for estimating the number of people who travel in a train with 20 passenger coaches?



ID 3895

Think Outside The Box Wikipedia says that the equator is about 40,075 kilometers (24,901 miles) long; 78.7% is across water and 21.3% is over land.

A yard was defined as the distance from finger tip to nose with the arms straight out to the sides.
Allowing 5 inches for a palm grip at each side we have 2(36-5) = 62 inches or 1.6m.

Estimate the number of people who holding hands in a human chain cover the length of the equator.



ID 3907

Think Outside The Box Which number goes next?

1 3 6 10 ?



ID 3909

Think Outside The Box How many 1x1 squares fit into the large square with the side length 4.8?

Find the maximum possible number.



ID 3912

Think Outside The Box What is the 100th positive integer that is not divisible by 10?



ID 3914

Think Outside The Box Anna and Bill roll a six-sided die.
The first person to roll a six wins.
Anna rolls first, then Bill rolls the die.
If nobody wins, they change the order: Bill starts first and so on.

What is the ratio of Anna's and Bill chances?



ID 3919

Think Outside The Box There are 190 coconuts in a basket.
Sailors one after another take out half of them and one each time until one is left.

How many sailors are there?



ID 3923

Think Outside The Box The weights of each pair of these boxes are 98kg, 101kg, and 102kg.

What is the difference between the heaviest and the lightest box?



ID 3924

Think Outside The Box If regular stars are placed as shown to form a complete circle, how many stars are needed?



ID 3925

Think Outside The Box In a game, Anna and Bill take 1, 2, or 3 coins on each turn.
The player to take the last coin from the pile wins.

If Anna goes first and there are 40 coins on the table, how many coins should she take to guarantee that she would win?



ID 3941

Think Outside The Box What fraction of this regular octagon is shaded?



ID 3946

Think Outside The Box You can throw an unlimited number of darts at the dartboard.
Some total scores are impossible to obtain, such as all the numbers less than 5 as well as 6, 8, and 9.

What is the highest whole number score that is impossible to obtain?

The Dart Problem by Bill Graham in Games Magazine (August 2003)



ID 3952

Think Outside The Box How many sets of three consecutive integers whose product is equal to their sum are there?



ID 3954

Think Outside The Box In a city, sixty percent of the men are married to eighty percent of the women.

Estimate the percentage of the married adults in the city.



ID 3961

Think Outside The Box Which year has had the greatest number of Roman numerals in it?



ID 3971

Think Outside The Box How many "yes or no" questions are needed to guess any 3-digit lock code?



ID 3974

Think Outside The Box Which result ends in exactly seven zeroes.

Remember: N! = 1 x 2 x . . . x N



ID 3978

Think Outside The Box The product and sum of two positive integers X and Y are added together. The result is 224.

How many different sets of X and Y exist?



ID 4004

Think Outside The Box The wind in the open-air swimming pool increases the westward swimming speed and decreases the eastward swimming speed by 1 mile per hour.

Will this swim take more or less time than the swim without the wind?



ID 4030

Think Outside The Box You roll two dice.

Estimate the expected value on the highest valued die?



ID 4031

Think Outside The Box If John walks up an escalator at a rate of one step per second, 12 steps take him to the top.
If John goes up at two steps per second, he reaches the top in 20 steps.

How many steps are there on the escalator?

Inspired by A. Dunn, Mathematical Baffles, Dover Publications, 1980, p 17



ID 4032

Think Outside The Box Two proofreading programs, A and B, discovered 30 and 40 errors, respectively.
There are 10 errors in common.
Estimate the number of errors that are still undetected.



ID 4033

Think Outside The Box On an island, three-quarters of the men are married to four-fifths of the women.

What is the minimum possible number of people on the island?



ID 4037

Think Outside The Box After a test of a code, John detected 2 errors and Mary discovered 3 errors in the same code.
There is one error in common.
Estimate the number of errors that are still undetected.



ID 4043

Think Outside The Box If you were to spell out the numbers, how far would you have to go before encountering the letter 'g'?



ID 4120

Think Outside The Box A father has left 47 donkeys for you to distribute to his three sons;
1/2 (23.5) should go to his eldest son,
1/3 (15.667) to the middle one, and
1/8 (5.875) to the youngest.

You arrive with your own donkeys.
You can add or take some donkeys from the herd.

How do you divide them so that all sons are happy with your decision?
How many donkeys does the eldest son get?

Inspired by Malba Tahan “The man who counted.”



ID 4128

Think Outside The Box Find the logic:

12345678 → 4
  234567   → 2
   3456      → 2
     45        → X

Find X.



ID 4141

Think Outside The Box One quarter of the competitors were faster than Mary and I, but two thirds were slower.

How many people were swimming?



ID 4160

ID 4164

Think Outside The Box One by one, 40 cars enter a company parking lot with 40 assigned places.
The first driver forgets his place number and takes a random place.
The remaining drivers take their assigned place, if available, or take a random place.

What’s the probability that the last driver ends up in his original assigned place?

Inspired by Peter Winkler's airplane problem.



ID 4165

Think Outside The Box Five students Anna, Bill, Craig, Daniel, and Eugene commute by bus. Every morning each student independently and randomly selects to board one of the 4 buses.
What is the average number of students in the bus that Anna chooses?



ID 4168

Think Outside The Box You pay $6 to enter a game.
You roll 2 dice.
You then have two choices: you can cash out and get paid the dollar amount of the roll, or you can pay $1 to roll the dice again.

What is your final gain per game if you play many times and choose the strategy to stop once you get more than 6 on two dice?



ID 4169

Think Outside The Box How many uninteresting numbers exist?

The question is based on the interesting number paradox, which is a semi-humorous paradox, which arises from the attempt to classify natural numbers as "interesting" or "dull."



ID 4205

Think Outside The Box There is an equal number of boys and girls.
Share $10 among them so that each girl gets $1 more than each boy.

How much does each girl get?



ID 4228

Think Outside The Box How many sets are there of three consecutive positive integers whose product is equal to their sum?



ID 4235

Think Outside The Box If the sum of 999 positive integers is equal to 1000 what is their product?



ID 4236

Think Outside The Box What is the maximum possible difference between the two-digit number and the sum of its digits?



ID 4297

ID 4303

Think Outside The Box The difference of two positive integers is equal to their average.

What is their ratio?



ID 4306

ID 4307

Think Outside The Box The amount of water flowing into a tank doubles every minute.
The tank is full in an hour.

When was the tank a quarter full?



ID 4308

Think Outside The Box A pirate boat is floating on a lake.
The pirates throw a heavy chest with gold coins overboard.

What happens with the water in the lake with respect to the shore?



ID 4326

Think Outside The Box I have 33 coins.

What is the minimum number of coins I need in order to make sure that each coin touches exactly three other coins?



ID 4338

Think Outside The Box There are 5 children in a boat.
Four of them do one of the activities below.

What is the fifth kid doing?



ID 4340

Think Outside The Box The product of two integers is 1000.
Neither of the numbers contains a zero.

Find the sum of the integers.



ID 4354

Think Outside The Box Len's number is 31.
Jim's number is 32.
Sam's number is 33.


Which number is the largest?



ID 4357

Think Outside The Box Seven trees are planted in a park, with exactly 3 meters between each successive planting.
In other words the second tree is 3 m from the first tree.
The third tree is 3 m from the second tree and so on.

What is the minimum possible distance between the first and the seventh trees?



ID 4386

Think Outside The Box Which is a better fit?

The smaller the percentage of the ‘area left over,’ the better the fit.



ID 4405

Think Outside The Box Once upon a time, there were three little pigs - ages 2, 4, and 6 months.
If one was born in January, when was one of his brothers born?



ID 4421

Think Outside The Box "This is a capital letter of the alphabet that's been folded just once.

Which letter is it if I unfold it? "

The puzzle was created by puzzlemaster Scott Kim



ID 4423

Think Outside The Box I multiply the ages of three kids and get 48.

If I add their ages, what is the smallest possible sum I might get?



ID 4424

Think Outside The Box What is the most money you can have in $1, $2, $5, $10, $20, and $50 bills and not be able to make exact change for a $100 bill?

Source: The Little Book of Big Mind Binders by Scott Kim



ID 4427

Think Outside The Box Three overlapping squares form 5 squares including themselves in the picture.

What is the greatest number of squares you can make by overlapping three squares of the same size?



ID 4428

Think Outside The Box You have a large supply of 5kg and 12kg weights.
Six 5kg weights and one 12kg weight have an average weight of 6kg.

What is the minimum number of weights that have an average weight of 7kg?



ID 4444

Think Outside The Box The diagram shows the lowest point and the highest point of our planet.

What place is the closer for John who lives in London?

Source: Nelson Thornes New Maths in Action. 2004



ID 4480

Think Outside The Box A car traveling with speed 12 meters per second decelerates uniformly until it comes to rest for 4 seconds.

What is the total distance the car travels as it decelerates?



ID 4495

Think Outside The Box If I place a pair of brackets in to this number expression, what result can be obtained?



ID 4504

Think Outside The Box If each coconut is priced at $9, then the shopkeeper loses $11.
If each coconut is priced at $11, then the shopkeeper gains a profit of $9.

How many coconuts are there?



ID 4510

Think Outside The Box Bob used to weigh 100kg.
His new stressful job causes him to lose 10% every month.

How much does he weigh after 3 months of work?



ID 4511

Think Outside The Box I composed the numbers from strips of paper.

Find the odd one out.



ID 4512

Think Outside The Box I composed the numbers from strips of paper.

Find the odd one out.



ID 4513

Think Outside The Box Which number required the most paper?



ID 4527

ID 4537

Think Outside The Box January 1st, 2014 was a Wednesday.

How many Wednesdays occurred in 2014?

2014 was not a leap year.



ID 4541

Think Outside The Box Gerry's circular garden is 1200 m in diameter and has no fence.

How far can a wolf run into the garden?



ID 4542

Think Outside The Box What is the maximum number of sections into which a pancake may be divided by four straight cuts through it?

(NOTE: The pieces cannot be re-arranged between cuts.)



ID 4566

Think Outside The Box How many 9s are there in the result of the multiplication:

12345 x 99999 ?

Don't use the calculator.



ID 4567

Think Outside The Box How many 1s are there in the result of the multiplication:

12345 x 99999?

Don't use a calculator.



ID 4569

Think Outside The Box If Gerry gives Jane one apple, they will have the same number of apples.

If Jane gives Gerry one apple, he will have twice as many apples as she has.

How many apples do they have?

Gerry is a gentleman and so always gives Jane apples.



ID 4575

Think Outside The Box After an hour, Evguenia catches and frees 10 fish.

If there are 100 fish in a lake how many fish remain uncaught after 5 hours?



ID 4583

Think Outside The Box Which regular shape cannot be used to tile a floor with no gaps between tiles?



ID 4596

Think Outside The Box How many 3x3 squares are there on a chessboard?



ID 4610

ID 4624

Think Outside The Box What is the word coiled inside this circle?



ID 4625

Think Outside The Box What is the word coiled inside this circle?



ID 4630

ID 4631

Think Outside The Box Which of the following is least like the others?



ID 4633

Think Outside The Box How many letters are there in the word that all smart students spell incorrectly?



ID 4647

Think Outside The Box Three positive whole numbers have the same answer added together or when multiplied together.

How many sets of such numbers exist?



ID 4649

Think Outside The Box A grandmother prepared bowls of fruit for her family. The only fruits available to her were cherries, apricots and red currants. Of course no bowl was empty and each bowl contained one kind of fruit.

All but five bowls contain some cherries,
all but four contain some apricots, and
all but three contain some red currants.

How many bowls were at the dinner?



ID 4657

Think Outside The Box The numbers show the areas of corresponding triangles.

What is the area of the rectangle?



ID 4659

Think Outside The Box 95.8% of James' classmates have different numbers of hairs than he has.

How many students are there in his class?



ID 4662

Think Outside The Box How many students are there in Evguenia's class, if 5% of the students have the exact number of hairs that she has?



ID 4665

Think Outside The Box If you make one word using each letter below only once, what place does the letter e take?


e r t s s s



ID 4669

Think Outside The Box John is Jim's son.
Jay is John's son.
John is a doctor's son.
His father is not a doctor.

Who is the doctor?



ID 4674

Think Outside The Box Using eight eights and addition only, make 1000.

How many times did you use sign plus (+)?



ID 4681

Think Outside The Box Gerry and Jane spent a week on an island and they ate only coconuts.
Gerry had already eaten half of the coconuts when Jane ate half of the remaining coconuts plus four more.
There are no coconuts left.

How many coconuts did they have?



ID 4692

Think Outside The Box What is the smallest integer that can be written with two digits?



ID 4703

Think Outside The Box On average there are 100,000 strands of hair on a person's head.
Hair grows at a rate of about 15cm a year and each hair lasts up to 6 years before it falls out.

If two sisters have 222,222 strands of hair together, and one has 20% more hair than the other, what is correct?



ID 4704

ID 4705

Think Outside The Box What gives the smallest result?

Here we write 0.333 . . . as notation for 0.3 recurring.



ID 4730

Think Outside The Box In a room, there are 3 bosses, 2 wives, and a plumber who works for the government.

What is the least possible number of people in there?



ID 4731

ID 4734

Think Outside The Box How many different bracelets can you make from four beads?



ID 4786

Think Outside The Box What is the sum of the first 100 prime numbers?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.



ID 4817

Think Outside The Box Gerry's income is seven-eighths that of Jane.
Gerry's expenses are seven-eighths those of Jane.
They spend less than they earn.

Jane promised to marry Gerry if he saves more than she does.

Who saves more money?



ID 4823

Think Outside The Box The sum of 11 consecutive integer numbers is 11.

What is the largest number?



ID 4830

Think Outside The Box The product of 33 positive integers is 33.

What is the sum of the numbers?



ID 4872

Think Outside The Box Crazy Logic. Choose a number.



ID 4880

Think Outside The Box If you were to spell out the numbers, how far would you have to go before encountering the letter 'A'?



ID 4886

Think Outside The Box Two American coins add up to 35 cents but one of them is not a dime.

What is the coin?

Penny = 1 cent.
Nickel = 5 cents.
Dime = 10 cents.
Quarter = 25 cents.



ID 4887

Think Outside The Box What is half of work and one third of gentleman?



ID 4888

Think Outside The Box If you take one third of GOOGLE and two thirds of ATT, what do you get?



ID 4891

Think Outside The Box A shopkeeper of a Dairy stands six feet tall and wears size 13 sneakers.

What does he weigh?



ID 4910

ID 4924

Think Outside The Box Zac's number is 5.
Anna's number is 6.
Bill’s number is 7.

What is Charlie's number?



ID 4930

Think Outside The Box If today is the payday in Bob’s company, what happens in two days?



ID 4942

Think Outside The Box If

One, Nine, and Eight gives ONE

what is

Two, Eight, and Nine ?



ID 4953

Think Outside The Box 300 plus 150 and 300 minus X is the same thing.

What is X?



ID 4969

Think Outside The Box Which number goes next?

1 1 2 3 5



ID 4979

Think Outside The Box When Pinocchio lies, his nose gets twice as long.
When he tells the truth, his nose gets 1 cm shorter.

His nose was 1 cm long in the morning, and it is 10 cm long in the evening.

What is the least number of times he could have opened his mouth today?



ID 5007

Think Outside The Box What letter goes next?

A E F H I K L M N



ID 5017

Think Outside The Box The difference between a positive integer and the sum of its digits is always divisible by . . .



ID 5026

Think Outside The Box 0.123123123123123 . . . .
What fraction is it?



ID 5046

Think Outside The Box You have more shoes than an average child in your country.

This statement is . . .



ID 5050

Think Outside The Box In a room, there are 3 bosses, 2 wives, and a plumber.

What is the least possible number of people in there?



ID 5061

Think Outside The Box 0.999 . . . means infinitely repeating decimals.

What is the largest result?



ID 5068

Think Outside The Box I add blue blocks one by one on the top.
Does the structure fail?



ID 5108

Think Outside The Box John cuts a large piece of cheese into small pieces using straight cuts from a very sharp cheese wire.
He does not move the pieces from the original shape while he cuts the cheese.

How many small pieces of cheese can he get using only five cuts?



ID 5129

Think Outside The Box Two men and two women want to cross a river.

The boat will only hold one man or two women.
How many times does the boat cross the river?

Find the minimum number.



ID 5137

Think Outside The Box A girl walked along a level road and up a hill from home and back.
Her pace on the level is 4 km an hour, uphill 3 km, and downhill 6 km.

How much time does it take if the total distance is 20 km?

Inspired by Lewis Carroll's Tangled Tale



ID 5140

Think Outside The Box A magic square is an arrangement of integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the diagonals, all add up to the same number.

Place numbers 13, 14, 15, and 16 in the square to make a magic square.

Which number do you place in the top left cell?



ID 5145

Think Outside The Box There are 10 coins and 5 of them are fake.
The real gold coins have the same weight, while all fake coins have different weights and each fake coin is lighter than a real one.

How many times do you use a balance to find all real coins?

Find the best strategy and the least possible number of weighings in the worst case.



ID 5152

Think Outside The Box There are two gods named Orbis and Fidelis, one on your left, the other on your right, but you do not know which is which. Fidelis always answers correctly. Orbis only answers alternate questions correctly; you do not know if his last answer was correct.

You must determine which god is which using the minimum number of YES/NO questions. How many questions do you need to be certain?

To clarify the matter, if Orbis is answering incorrectly your entire question is evaluated correctly and then the answer is reversed. A single question to both gods counts as two questions.

Author : Leslie Green

Inspired by G. Boolos. 'The hardest logic puzzle ever', The Harvard Review of Philosophy (6), 1996.



ID 5234

Think Outside The Box There are two gods named Mendax and Fidelis, one on your left, the other on your right, but you do not know which is which. Fidelis always answers correctly. Mendax only answers one question in 7 correctly in a repeating cycle. You do not know which part of the cycle Mendax is currently on.

You must determine which god is which using the minimum number of YES/NO questions. How many questions do you need to be certain?

To clarify the matter, if Mendax is answering incorrectly, your entire question is evaluated correctly and then the answer is reversed. A single question to both gods counts as two questions.

Author : Leslie Green

Inspired by G. Boolos. 'The hardest logic puzzle ever', The Harvard Review of Philosophy (6), 1996.



ID 5438

Think Outside The Box The boss of a 10 person company is always the last to arrive, and gets the worst of the 10 car parking places as a result. Being the boss, he decides to allocate parking places to each of his 9 employees (all of whom use a car to get to work), obviously keeping the best parking place for himself.

The employees already hate the boss, who only got the job by marrying the owner. Further enraged by the new rule, they collectively decide to ignore it and just park randomly when they arrive. All places are good for the employees.

What is the chance that the boss gets to park in the best parking place?

Author: Leslie Green



ID 5472

Think Outside The Box What is the main difference between the pictures on the left page and on the right page?

The problem is similar to 100 Bongard Problems on visual pattern recognition.

M. Bongard (1924 – 1971) was a computer scientist. His tests played an important role in the disciplines of cognitive psychology and cognitive science.



ID 5474

Think Outside The Box What is the main difference between the pictures on the left page and on the right page?

The problem is similar to 100 Bongard Problems on visual pattern recognition.

M. Bongard (1924 – 1971) was a computer scientist. His tests played an important role in the disciplines of cognitive psychology and cognitive science.



ID 5478

Think Outside The Box What is the main difference between the pictures on the left page and on the right page?

The problem is similar to 100 Bongard Problems on visual pattern recognition.

M. Bongard (1924 – 1971) was a computer scientist. His tests played an important role in the disciplines of cognitive psychology and cognitive science.



ID 5482

Think Outside The Box What is the main difference between the pictures on the left page and on the right page?

The problem is similar to 100 Bongard Problems on visual pattern recognition.



ID 5533

Think Outside The Box Gerry picks up several coins from the pirate chest. All but 5 have an eagle. All but five are silver. All but 5 are at least 100 years old.

What is the minimum number of coins in his collection?



ID 5582

Think Outside The Box The Bermuda Triangle, also known as the Devil's Triangle, is a loosely defined region, where a number of aircraft and ships are said to have disappeared under mysterious circumstances. The triangle's three vertices are in Miami, Florida peninsula; in San Juan, Puerto Rico; and in the mid-Atlantic island of Bermuda.

The distance from Miami to Bermuda is 1668 km.
The distance from Miami to Puerto Rico is 1663 km.
The distance from Puerto Rico to Bermuda is 1571 km.
Estimate the surface area of the famous triangle.



ID 5614

Think Outside The Box Alec, Beatrice, Crystal and Douglas opened their Christmas presents.

Alec opened 3 presents.
Beatrice opened 5 presents.
Crystal opened 12 presents.

How many presents were opened by Douglas?



ID 5617

Think Outside The Box Brainteaser: A word becomes shorter when you add two letters to it.

How many letter are there in the word?



ID 5622

Think Outside The Box These are two identical six‐sided dice. The opposite faces of a die add up to 7.

What is the sum of the number of dots on the two faces that touch each other?



ID 5665

Think Outside The Box What is the units digit of the product of all positive two-digit integers which are evenly divisible by 11?



ID 5673

Think Outside The Box The teacher walked into her classroom to find a scene of devastation. There was red paint on the walls, her lunch had been half eaten, and books were thrown around the room. There were only three children in the room: Alex, Betty, and Clive.
All three said that Betty ate the lunch. Betty said Alex painted the wall.
Clive said that Alex threw the books. Alex said that Clive painted the walls.

The Headmaster was called in to resolve the crisis. On his way to the scene he found Wesley hiding in the corridor. Whilst Wesley would not directly implicate anyone, he did admit (under duress) that each of the three had done one of the crimes, and that every statement they made had been untrue.

Given that Wesley is telling the truth, who threw the books?

Author: Leslie Green



ID 5681

Think Outside The Box A white hen lays an egg every third day.
A black hen lays an egg every second day.

How many eggs in total do a white hen and a black hen lay in November?



ID 5695

Think Outside The Box Find the difference of two different integers X and Y
if
XY = YX



ID 5745

Think Outside The Box Several students (N) randomly choose their places on a bench.

What are the chances for Gerry to be sitting next to Jane?



ID 5796

Think Outside The Box A dog runs over a field.
He passes hens and cows.
He sees three times as many hens as cows.

Which of the following could be the total number of feet he saw?



ID 5836

Think Outside The Box ONE + ONE =

You can add zero(s) where you want.

What can be the result?



ID 5841

Think Outside The Box There are 100 prisoners in a city prison.

Every week a new prisoner comes in and half or less of them leave the prison.

How much time passes till the moment when there are no prisoners in the prison?



ID 5843

Think Outside The Box The first four Volumes of an Encyclopedia are stacked vertically side by side on a shelf. The thickness of a Volume is 10cm, and the thickness of the two covers of each Volume is 1cm.

What is the distance from the first page of Volume I to the final page of Volume IV?



ID 5854

Think Outside The Box Anna, Bob, Cindy, and Daniel have correspondingly 50%, 60%, 70%, and 80% chances of knowing how to solve each problem correctly in the next test. They know which problem they can and cannot solve.

What average score do they expect to get if they take the test in pairs, which they wisely choose?



ID 5857

Think Outside The Box I take off from Brussels, Belgium and fly 777 miles due south. Then, I turn the plane and fly 777 miles due west. I turn again and fly 777 miles due north, and finally turn and fly 777 miles due east.

Which country do I land in?



ID 5862

Think Outside The Box Achilles and the Tortoise

The Paradox of Achilles and the Tortoise was described by the Greek philosopher Zeno of Elea in the 5th century BC. The great hero Achilles challenges a tortoise to a footrace. He agrees to give the tortoise a head start of 100m. When the race begins, Achilles starts running, so that by the time he has reached the 100m mark, the tortoise has only walked 10m. But by the time Achilles has reached the 110m mark, the tortoise has walked another 1m. By the time he has reached the 111m mark, the tortoise has walked another 0.1m, then 0.01m, then 0.001m, and so on. The tortoise always moves forwards while Achilles always plays catch up.

Why is Achilles always behind the tortoise?



ID 5863

Think Outside The Box Choose a word that ends, includes and starts with letters E, N, D correspondingly.



ID 5867

Think Outside The Box This is a part of a chessboard.

What area is larger?



ID 5901

Think Outside The Box The Two Envelope Paradox

One envelope has twice as much money as the second one. Gerry does not know which envelope contains the larger amount.
He takes one of the envelopes, counts the money, and is offered the chance to switch the envelope.

He thinks "If the amount of money in the chosen envelope is X dollars, then the other envelope contains either 2X of 0.5X dollars, with equal probability of 0.5. The expected value of switching is 0.5 (2X) + 0.5 (0.5X) = 1.25X. This is greater than the value in the initially chosen envelope. It is better to switch."

What is your advice?



ID 5964

Think Outside The Box A 99-people city chooses its mayor between Anna and Bill.
They have a strange rule: the first person chooses a candidate and the next two people always choose another one and so on. If the first person casts a ballot not marking anything at all, the next two people choose whatever they want.

What is the best strategy for Anna to win if she starts first?



ID 5965

Think Outside The Box 72 - 52 = 40

Which digit should be moved to make the above equation correct?



ID 5966

Think Outside The Box The picture shows a crescent.

What is the minimum number of lines needed to divide it into 6 parts?



ID 5990

Think Outside The Box Barber paradox

In a city, the barber is the 'one who shaves all those, and those only, who do not shave themselves.'

Who shaves the barber?


A barber (from the Latin barba, 'beard') cuts, dresses, grooms, styles and shaves men's and boys' hair.



ID 5992

Think Outside The Box What is the sum of the interior angles of the Bermuda triangle?



ID 6008

Think Outside The Box The ball's design stitches together hexagons with pentagons. The ball made its World Cup debut as Adidas' Telstar in 1970 in Mexico. The ball's pattern of white hexagons with black pentagons made it easily visible on television.

If there are 12 pentagons, how many hexagons are there?



ID 6009

Think Outside The Box Pop Quiz Paradox

A teacher announces to his class that there will be a quiz one day during the next week. The teacher gives the definition that they would not know when they came in to class that the quiz was going to be given that day.
The brightest student says that the quiz cannot be on Friday because they will know the day on Friday. With the same technique, she eliminates Thursday, then Wednesday, Tuesday and Monday.
"You cannot possibly give us a pop quiz next week," she says.

When does the teacher give the pop quiz?

I know the paradox from Charles Carter Wald. Probably, Martin Gardner described the quiz for the first time in The Colossal Book of Mathematics.



ID 6042

Think Outside The Box Leslie Green asks:

An American salesman flies over to London (UK) and for reasons best known to himself carelessly steps out of a first floor window. He breaks his leg.

Why?



ID 6051

Think Outside The Box Leslie Green tells a story and asks:

A elderly monk is arranging the annual charitable gift. He will put bank notes in two envelopes such that one envelope has twice the amount in the other. The number of notes will be undetectable within the heavy envelope. It is required that anyone who opens an envelope does not know if they have the high amount or the low amount.

Given that the bank notes available to the monk only occur in units of $1, $2, $5, and $10, which statement is acceptable?

Inspired by a comment from Jeff Jordan concerning Two Envelope Paradox



ID 6071

Think Outside The Box Logic puzzle.

If I remove one I get one more. What do I have at the beginning?



ID 6072

Think Outside The Box Logic puzzle.

What can you put into the eight empty boxes?



ID 6075

Think Outside The Box The sum of the digits of a seven-digit even integer is 7.

What is the product of these digits?



ID 6107

Think Outside The Box Kitty has 2017 marbles. The marbles are numbered from 1 to 2017. Marbles with equal digit sums have the same color.

How many different colors of marbles does Kitty have?



ID 6126

Think Outside The Box Roman numerals are a numeral system of Ancient Rome based on letters of the alphabet.

For example, CVII is 107 (100 + 7).

What number cannot be represented in Roman numerals?



ID 6128

ID 6193

Think Outside The Box The discus throw men's Olympic record is 69.89 m and the women's Olympic record is 72.30 m.

Make a logical conclusion as to why the men's record is smaller than the women's record.



ID 6288

Think Outside The Box How many eggs can the hens put in an empty basket?



ID 6292

Think Outside The Box If it is raining at midnight in an old English town, what are the chances of the sun shining in 100 hours time?



ID 6297

Think Outside The Box Logic Puzzle.

Many years ago a king of a North European country decided to establish which is more dangerous for health: tea or coffee.
He ordered that one prisoner should only be given coffee, and that another prisoner should only be given tea.

What do you think? Who died first?



ID 6329

Think Outside The Box In a spy code, the digits 2 8 9 means 10.

What does 1 9 8 mean?



ID 6334

Think Outside The Box Alex has mathematics class 4 times a week.

If there is mathematics class
8:00 on Monday,
8:55 on Tuesday,
9:50 on Wednesday, and
10:45 on Thursday,
when is it on Friday?



ID 6382

Think Outside The Box The letter "o" is used ______ times in this sentence.



ID 6452

Think Outside The Box I saw the wrist watch of my friend in the rear view mirror of my car. The picture shows what I saw.

What was the time at that moment?



ID 6457

Think Outside The Box If certain words in this question are spelt wrong, how many of the eighteen words are spelt wrong?



ID 6477

Think Outside The Box A tap drips one drop of water every second.
It takes 3000 such drops to fill a 200-ml glass.

How many drops of water can you put in an empty 50-ml glass?



ID 6500

Think Outside The Box The St. Petersburg paradox was solved by Daniel Bernoulli in 1738.

A casino staff member tosses a coin repeatedly until it comes up heads. If heads appears on the first throw, the casino pays you $2. If it appears on the second throw, you receive $4; if on the third, you receive $8 and so on, doubling each time.

How much would the casino be willing to accept from you to consider the game favorable for it?



ID 6501

Think Outside The Box A girl takes 3 identical ropes, mixes the ends, and asks her boy-friend to tie three pairs of knots on the top.
There is a superstitious tradition in their region that if the result is a ring with all three ropes, then their relationship will be long.

According to this tradition, what are chances of them getting a long relationship?



ID 6562

Think Outside The Box How many letters are there in the word which becomes shorter after adding two letters at the end?



ID 6611

Think Outside The Box If it were four hours earlier, it would be twice as long until midnight as it would be if it were four hours later.

What time is it now?



ID 6617

Think Outside The Box Firefighters are taught to put on their pants in three seconds.

How many pairs of pants can a well-trained fireman put on in a minute?



ID 6814

ID 6947

Think Outside The Box Jane's handkerchief has a regular pattern.

What percentage of her handkerchief is red?



ID 6950

Think Outside The Box Anna, Betty and Cindy have apples.
Betty gives half of her apples to Cindy, Cindy gives 6 apples to Anna, and Anna gives 2 apples to Betty.
Now each of them has the same number of apples - 10.

How many apples did Anna have initially?



ID 6974

Think Outside The Box Gerry has 32 pounds of gold in small pieces.
What is the minimum number of times he uses the balance scale with two pans to measure out 12 pounds of the gold?



ID 7003

Think Outside The Box If Jane ate 1 blue berry from each row, and then Gerry ate 1 blue berry from each line, how many berries had been left?



ID 7030

Think Outside The Box A claustrophobic gentleman chooses his place in the train that will enter a tunnel just after the station.

Where is the best place for him?



ID 7065

Think Outside The Box A rich father gave the eldest son half of his gold ingots plus an extra ingot.
Then he gave the second son half of what was left plus an extra ingot.
Finally he gave the youngest son half of what was left plus an extra ingot.
He then had no gold left.

How many ingots did the rich man have?



ID 7076

Think Outside The Box Two coins have the diameters of 30mm and 15mm.

The small coin rolls around the fixed big coin until it returns to its starting position.

How many revolutions of the small coin are there in total?



ID 7079

Think Outside The Box Logic Puzzle

Two fathers, two sons, and two doctors had a healthy breakfast.
Each person ate an apple.

What is the least possible number of apples that have been eaten?



ID 7160

Think Outside The Box Leslie Green asks:

What is the secret message in the text below?

Mary Evans eventually took Michael, Ewan, and Tom Maudsley into Downton, not into Glasgow’s heavy traffic.



ID 7261

Think Outside The Box Never judge by appearances

Which of the following is closest in meaning?



ID 7262

ID 7295

Think Outside The Box Something gets wetter the more it dries.

What is the first letter of it?



ID 7296

Think Outside The Box Something is more useful when broken. Find an example.

What is the first letter of it?



ID 7371

Think Outside The Box Alcuin, Abbot of Canterbury (AD 735-804) and one of the first English puzzlemakers asked "If 100 bushels of corn were distributed among 100 people in such a manner that each man received three bushels, each woman two, and each child half a bushel, how many men, women, and children were there?"

There are many different correct answers. If the number of men, women, and children are as close to each other as possible, what is the number of children?



ID 7440

Think Outside The Box Ninety percent of 650 Members of Parliament (MPs) voted either YES or NO on an important bill.
The speaker declares that there are more YES votes by a certain number.

What number can the opposition consider as incorrect?



ID 7491

Think Outside The Box Educational researchers have established that some students (who have very limited understanding) just take numbers presented in mathematical problems and almost randomly combine them, with little understanding of what they are doing.

There are 5 boys in a class. John likes Julie and Helen. Julie likes Peter, and 6 other boys. Mark is not in the classroom, but Helen is. There are 3 girls in the class with the 5 boys.

How many boys does Helen like?

by Leslie Green



ID 7493

Think Outside The Box In a family, each child has at least one brother and one sister.

What is the least possible number of children in the family?



ID 7555

Think Outside The Box Gerry has several European coins in his pocket.
If Gerry takes any three coins he certainly gets one 2-cent coin.
If Gerry takes any four coins he certainly gets one 1-cent coin.

How much money is it if he takes 5 coins?



ID 7609

Think Outside The Box Leslie Green asks:

American English and British English are similar, but despite global communications they don't seem to be rapidly converging to a common language. Minor spelling changes, like omitting the letter 'u' here and there, or using an 's' in place of a 'z' would not cause problems, but sometimes words can mean quite different things.

Which pairs are not the same thing?



ID 7638

Think Outside The Box Twenty girls sit on a bench. The first girl tells a number to the second girl and she tells another number to the next girl.

If the first girl starts with 20 and each next girl either adds one to the number she received or subtracts one from it, what is the possible final result?



ID 7681

Think Outside The Box A girl is facing a flat (planar) mirror in front of her.

What is the minimum possible height of the mirror in order for her to see herself entirely in the mirror?



ID 7695

Think Outside The Box John, his father, and his mother play table tennis. After two of them play a game, the winner stays and plays with the third member of the family. This pattern continues for each new game.

At the end of the evening John reported that he had played 7 times, whilst both his father and mother had played 6 times each. Comment on this report.



ID 7716

Think Outside The Box If the only brother of John's father's only sister has an only child, what would be relationship between the child and John?



ID 7748

Think Outside The Box The sign on the bumper of a car reads CH.

What European country is it?



ID 7749

Think Outside The Box The International Air Transport Association (IATA) supports aviation with global standards for airline safety, security, efficiency and sustainability.

Each airport has an IATA three-letter code.

Which city's airport has the code LAX?



ID 7765

ID 7807

Think Outside The Box  FOUR + FIVE = NINE

Each letter represents a unique digit in the cryptarithm.

What is the smallest possible value for NINE?



ID 7822

Think Outside The Box Mary saw 5 crows walking on a newly seeded lawn.
John saw 4 crows walking there.

How many crows had walked on the lawn?



ID 7839

Think Outside The Box Jane has rabbits, kittens, and chickens.

All of them are rabbits except three, all of them are kittens except four, and all of them are chickens except three.

How many pets does she have?



ID 7853

Think Outside The Box The terms anno Domini (AD) and before Christ (BC) are used to label the number of years in the Julian and Gregorian calendars. The term anno Domini is Medieval Latin and it is taken from the original phrase "anno Domini nostri Jesu Christi", which translates to "in the year of our Lord Jesus Christ".

An archaeologist finds three coins with different notations.

Which coin is fake?



ID 7871

Think Outside The Box One hundred coins from the piggy bank can be evenly divided among kids and their Granny.

The coins are also evenly divided among the kids.

How many more coins does each kid get if their grandmother refuses her share?



ID 8008

Think Outside The Box A clock fell to the ground.

What time is it?



ID 8045

Think Outside The Box Twenty-five students took a test and each got a score of either 3, 4, or 5.

How many more 5s than 3s were there if the sum of all scores was 106?

This is a Russian Olympiad problem for 8th grade at problems.ru.



ID 8102

ID 8105

Think Outside The Box Can you fill the blank?



There are ________ letters e in the sentence.



ID 8136

Think Outside The Box Gerry (60kg) uses the swing in his granny's garden every weekend.

At what distance between the two knots is the load in the rope the smallest?



ID 8142

Think Outside The Box The picture shows a road scheme. The road is full of cars that move from the left to the right.

At what point of the road scheme do the cars move at the greatest speed?



ID 8160

Think Outside The Box What total number of people can you be sure are not present in this scene?



ID 8177

Think Outside The Box Which is larger than the others?



ID 8179

Think Outside The Box Six points are randomly chosen at the edge of a pizza.

Three straight cuts are made by passing through two of the points, never the same.

What is the smallest possible number of pieces that can be made?



ID 8182

Think Outside The Box A magician tells you that if you correctly guess the exact value of money in an envelope then he will give you the money.

The envelope contains bills (notes) totalling between $1 and $10 (inclusive). After each guess he will tell you if your guess is too high or too low, or he will give you the money in the envelope. You can try only 3 times.

What is your best first guess?



ID 8201

Think Outside The Box Big Ben is the nickname for the Great Bell of the clock at the north end of the Palace of Westminster in London, United Kingdom. Big Ben is the hour bell. For example, at twelve o'clock, twelve chimes ring from the great bell in 44 seconds.

How long does it takes to ring the hours at 15:00 ?

You can listen to Big Ben by clicking on the link.



ID 8216

Think Outside The Box "300" costs $30;
"20" costs $20;

How much does "100" cost?



ID 8287

Think Outside The Box Atlantic tropical storms are named through a strict procedure by an international committee of the World Meteorological Organization.

Based on the given table, guess how the tenth hurricane in 2022 might be named.



ID 8305

Think Outside The Box What is the minimum number of straight cuts Gerry has to make in a 12 x 12 carpet so that it fits a room with dimensions 18 x 8?



ID 8307

Think Outside The Box Place 6 points on a plane to make as many as possible three-in-a-line rows.

What is the largest possible number of rows?

Inspired by a problem of Sam Loyd



ID 8308

Think Outside The Box I draw 4 three-in-a-line rows using 8 red points.

What is the smallest possible number of points to draw 4 three-in-a-line rows?

Inspired by a problem of Sam Loyd



ID 8310

Think Outside The Box A contractor planning the construction of a house found he would have to pay:

$1,100 to the paper hanger and the painter,
$1,700 to the painter and plumber,
$1,100 to the plumber and electrician,
$3,300 to the electrician and carpenter,
$5,300 to the carpenter and mason,
$3,200 to the mason and painter.

Who charges the largest amount for his work?

Source: More Mathematical Puzzles of Sam Loyd, Volume 2 by Martin Gardner, 1960



ID 8325

Think Outside The Box Continue the pattern to find the unknown value.



ID 8335

Think Outside The Box You have a two-pan balance scale and 12 identically looking coins. One of the coins is counterfeit and it can be either lighter or heavier than the others.

How many weighings do you need to determine the counterfeit coin?



ID 8349

Think Outside The Box How many mistakes are there on the blackboard?



ID 8352

Think Outside The Box A banker has a brother, who is a plumber. The plumber is married to a nurse and they have two children - two boys.

Which statement can be true?



ID 8414

Think Outside The Box Which letter comes next in the sequence?



ID 8415

Think Outside The Box Which letter comes next in the sequence?



ID 8422

Think Outside The Box I have a 'Christmas tree' that is green from both sides.

I would like to cut it into separate pieces and compose a rectangle.

What is the minimum possible number of straight cuts I should make?



ID 8425

Think Outside The Box Find the missing number.



ID 8469

Think Outside The Box There are 15 face-down cards on the table. There is an ace among them. You may choose a group of cards and ask if the ace is in the chosen group or not.

How many Yes-No answers do you need to detect the ace?

Choose the minimal possible number of questions.



ID 8473

ID 8476

ID 8478

Think Outside The Box There are 4 points on a line and a point outside the line.

What is the largest number of isosceles triangles I can form, provided that the points are optimally positioned?

Source: kvantik.com 2016



ID 8481

Think Outside The Box I fold a square piece of paper twice and cut it along the straight red line.
When it is unfolded, there is an equilateral triangle in the middle of the piece of paper.

If I need to obtain a square by a single straight cut in the same way, how many times do I need to fold a square piece of paper?



ID 8493

Think Outside The Box Gerry has 13 stones of different weights.

How many times does he use a balance scale to find the lightest stone and the heaviest stone?

Find the minimum number.



ID 8518

Think Outside The Box There is a mistake in one of the letters.

Which one?



ID 8522

Think Outside The Box I am nothing, not something.

You can see me only where I am not.

I am made from two things, yet I am still nothing.

 What am I?



ID 8567

Think Outside The Box Magic triangle

Place the numbers 1, 2, 3, 4, 5, 6 in the circles so that their sum on a side is the same.

What is the largest possible sum?



ID 8582

Think Outside The Box I have 1 yellow, 2 green, 3 red, and 4 blue cubes.

I built a tower so that no cubes of the same color touch each other.

Which color is the cube in the middle?



ID 8589

ID 8597

Think Outside The Box Which 3 do you move to make the phrase correct?



ID 8600

Think Outside The Box There is only one entrance into an apartment building via the ground floor.
One person lives on the first floor, two people live on the second floor, three on the third floor, four on the fourth floor, five on the fifth floor, six on the sixth floor, and one lives on the seventh floor.

Which button is more frequently used in the lift (elevator) of the building?



ID 8621

Think Outside The Box My doctor gave me 2 tablets for 2 days against flu, and 2 tablets for 2 days against headache. The flu tablets and headache tablets are supposed to be taken at the same time. Unfortunately I mixed the tablets.

Estimate the probability that I follow the doctor's instructions correctly.



ID 8626

Think Outside The Box There are 15 piles with 1, 2, . . . 15 coins.
For each step, I can take the same number of coins from any of the piles I choose. To be clear, at each step the number of coins can be changed.

If, for example, I decide to take 3 coins from selected piles, I cannot remove any coins from piles having less than 3 coins.

What is the minimum possible number of steps that is necessary to take all the coins?



ID 8669

Think Outside The Box The pyramid below is to be numbered so that
- each box contains a positive integer,
- apart from the top row the number in each box is the product of the numbers in the two boxes immediately below ;
- the numbers in a row are all different.

What is the smallest possible value of X?



ID 8672

Think Outside The Box Jane folded a square sheet of paper in half twice and then cut it twice, as shown in the diagram, before unfolding it all.

How many pieces does she obtain?



ID 8727

Think Outside The Box Balls numbered 1, 2, ... are put into a box as follows. At 1 minute to noon the balls numbered 1 to 10 inclusive are put in, then ball 1 is taken out. At 1/2 a minute to noon balls 11 to 20 are put in, then ball 2 is taken out. At 1/3 minute to noon balls 21 to 30 are put in, and ball 3 is taken out, and so on.

How many balls are in the box at noon?

adapted from A Mathematicians Miscellany by J.E. Littlewood (1953) by Leslie Green



ID 8741

Think Outside The Box Gerry has several pieces of wire of lengths 1 cm, 2 cm, 3 cm, 5 cm, 6 cm, 7 cm, 8 cm, and 9 cm.
He uses some of those pieces to form a wire model of a cube with side length 1 cm.
There must not be any overlapping wire sides, and the wires cannot be cut.

What is the smallest number of the wire pieces that can be used?



ID 8766

Think Outside The Box I want to delete some red points from the picture.

What is the maximum number of points that I can keep so that no three of them fall on a straight line?



ID 8767

Think Outside The Box Which ring do you cut so that all rings are separated?



ID 8773

Think Outside The Box An engineering company builds a road network connecting 6 cities that are at the same distance on a circle. The same number of people travel from each city to 5 other cities every day.

For which design of the roads the average distance that a person has to ride is the smallest?



ID 8776

ID 8838

Think Outside The Box Children eat fruits.
Everybody eats more than one piece, and 5 pieces less than the total eaten by all of the other children.

How many fruits have they eaten?



ID 8844

Think Outside The Box I want to connect the small red dots using only straight lines and without lifting the pen from the paper.

What is the minimum number of straight lines that connect the dots in such a way?



ID 8862

Think Outside The Box I multiply a number by 10 and get a prime number.
I multiply the same number by 15 and get another prime number.

How many such numbers are there?

A prime number is a positive integer that has no positive divisors other than 1 and itself.



ID 8869

Think Outside The Box I want to connect the small red dots using only straight lines and without lifting the pen from the paper.

What is the minimum number of straight lines that connect the dots in such a way?



ID 8931

Think Outside The Box Young girls collected apples in a garden.

January collected 31 apples.
Febe collected 28 apples.
March collected 31 apples.
April collected 30 apples.
May collected 31 apples.
. . .

How many apples did January, Febe, March, April, May, and June collect together?



ID 8938

Think Outside The Box There are several soldiers in a detachment.
Every evening three of them are on duty.

After a certain period of time each soldier has shared duty with every other exactly once.

What is the minimum possible number of soldiers in the detachment?



ID 8947

Think Outside The Box How many different ways are there from the top to the bottom?



ID 8985

Think Outside The Box A large cube is painted from all sides and then cut into 10 x 10 x 10 = 1000 small cubes.

How many of the small cubes are painted on just one side?



ID 8988

Think Outside The Box Five villages are connected by a circular road, so that the distance between two neighboring villages is 1 km.

One student lives in One Oak, two in Two Oaks, three in Three Oaks, four in Four Oaks, and five in Five Oaks.

In what village is it better to organize a summer camp so that the total distance for all students to walk from their home villages to the camp is minimized?



ID 8994

Think Outside The Box This is a standard set of dominoes.

I put all of them in a chain, for example 3 spots on one domino is connected to 3 spots on the next one.

If I have 2 spots on left end of the chain, what is the number of spots on the right end?



ID 8995

Think Outside The Box There are 3 hockey pucks on ice.
A player shoots one of them between the two others. Then he repeats the shots always choosing another puck. He shoots all three pucks.

After how many shots can he get back to the original positions of the three pucks?



ID 8999

Think Outside The Box Six friends equally share 5 apples by cutting the apples.

They can not cut an apple into more than than 5 pieces. Each apple has to be split into equally sized pieces, but this size can vary from apple to apple.

What is the total number of pieces?



ID 9004

Think Outside The Box There are 3 hockey pucks on ice.
A player shoots one of them between the two others. Then he repeats the shots always choosing another puck.

After how many shots can he get the same position of the three pucks?