ID 576

A river boat travels 2 km in 12 minutes with the current and 1 km in 18 minutes against the current.

Determine the speed of the boat.

ID 822

Three 250-ml glasses contain orange juice.
The first one is 2/3 full, the second is 5/6 full, and the third is 9/10 full.
Water is added to fill each glass completely.
All drinks are then poured into a large jar.
Which fraction of the mixture in the jar is orange juice?

ID 824

Three referees A, B and C are at the corners of a rectangular field.

At which point should the referees meet so that the time they walk to that point is minimized?

ID 827

What is the sum of 99 consecutive positive integers if the middle one is n?

ID 832

How many positive integers less than 111 are evenly divisible by either 2 or 3, or both?

ID 836

Many people stand in a line (queue) to buy tickets to a match.
There are enough tickets for each person to have two tickets.
Instead, every person in the beginning of the line buys three tickets until there are none left so 12 people are left without tickets.

How many people were there in the line to begin with?

ID 837

The sum of the consecutive integers from -33 to X, inclusive, is 105.

What is the value of X?

ID 844

A password consists of four digits and the repetition of digits is allowed.
Determine the number of different passwords that can be created.

ID 848

Sixteen European teams enter a football tournament.
Each team plays one match against each of the other teams with three points for a win, one point for a draw, and none for a defeat.

How many points can one team earn?

ID 850

In the first week John made \$1.
He made 5 times more than the previous week if the week was odd, and 2 times more if the week was even.

How many weeks did he work before becoming a millionaire?

ID 1006

Six post office employees are working today.
It takes one employee one minute to serve one person.

How long would you have to wait in the line if you hold number 321?

ID 1007

Anna and Beatrice ran a 100m race. When Anna crossed the finish line, Beatrice was 1m behind her.
In the next race, Beatrice started 1m ahead of the starting line.

If each of them runs at the same speed as in the previous race, who will cross the finish line first?

ID 1008

Twelve teams enter a tournament.
Each team plays one match against each of the other teams, with three points for a win, one point for a draw and none for a defeat.

How many ways are there for a team to score 12 points?

ID 1009

Here, a password consists of four digits, 0-9.

How many passwords are there that read the same backwards as forwards?

ID 1022

A password consists of five digits, 0-9.

How many passwords are there that read the same backwards as forwards?

ID 1030

Find two consecutive even integers such that the smaller added to two times the larger gives a sum of 22.

ID 1031

I took a picture of a six-sided die, whose faces are numbered from one to six.
I added the numbers of dots that I saw in the photo.

What are the maximum and minimum numbers I can get?

ID 1033

I don't quite remember my five-digit password.
The first and last digits are the same, 542 is in the middle, and the password is evenly divisible by 9.

What is the first digit?

ID 1039

What is the condition for the smallest ten-digit integer that has only two digits the same?

ID 1040

Anna traveled 3600km in a car.
She had six tires and changed them such that each tire was used over the same distance.

For how many kilometers was each tire used?

ID 1079

A family travels from their town to the nearest seashore at a speed of 30 km per hour, stays there 2 hours, and then returns at a speed of 60 km per hour.
The total round trip takes 12 hours.

What is the average speed for the driving part of the trip?

ID 1113

There is a total of 6 squares whose vertices are points on the rectangular 3 x 3 grid.
How many squares can you draw on the 4 x 4 grid in the same manner?

ID 1145

Gentlemen are evenly spaced in a circle and the 11th gentleman is directly opposite the 29th gentleman.

How many people are there altogether?

ID 1172

Based on 20 years per generation, estimate the number of ancestors you had 220 years ago, if none of them appears more than once in the list.

ID 1429

What number should replace the question mark?

ID 1443

From the offered options select the picture that logically best fits to the free cell.

ID 1446

Three children and two adults want to cross a river.
Their boat can carry only one adult or three children.
An empty boat cannot cross the river.

What is the minimum number of crossings to get the people to the other side?

ID 1547

For what value of x does the algorithm say C?

ID 1670

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

ID 1749

A password consists of two digits, from 1 to 4, followed by two capital letters from an alphabet having 25 letters.
Repetition of digits and letters is allowed.

Determine the number of different passwords that can be created.

ID 1831

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 1929

I have a collection of 44 songs that are each 4 minutes in length and 55 songs that are each 5 minutes in length.

What is the largest number of complete songs that I can play in 4.5 hours?

ID 2025

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 2044

The sum of ages of two brothers is 55 and the elder brother is 9 years older than his young brother.
The age of a brother is same as his brother's age with the digits reversed.

How old is the elder brother?

ID 2149

Please make 121 by using three 5s.
You can use any math operator that you would like.

How many times do you use the plus sign (+) in the expression?

ID 2177

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 2192

If a hen and a half lay one half of an egg in two days and a half, how many eggs does a hen lay in a month?

ID 2194

Find a phrase that differs from the others.

ID 2216

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 2219

A lot of money is in a box.

None or just one inscription on the boxes is true.

Guess where the money is.

ID 2221

I took several pieces of fruit from the bowls.
All of them are cherries except two, all of them are apricots except two, and all of them are red currants except two.

How many pieces of fruit did I take?

ID 2237

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 2240

In a group of 27 people, 17 have studied Japanese, 7 have studied Chinese, and 7 have not studied either.

How many of them have studied both Chinese and Japanese?

ID 2266

Neglecting the seconds hand, how many times do a clock's hands overlap in a day?

ID 2271

By using 1 2 3 4 once each and any arithmetical operations +, -, x, and /, what is the smallest number I cannot obtain?

For example: I can obtain 2: 3 x 2 x 1 - 4 = 2

Parentheses are not allowed.

ID 2286

John is 33 years, 33 months, 33 weeks, 33 days, and 33 hours old.

How old is he?

ID 3049

A melon slice weighs 5kg, and 92% of the weight is from water.
After lying in the sun, the water makes up 75% of the weight.

Estimate the new weight of the slice in kg.

ID 3087

John's dad pays him 75 cents for each correct answer he provides in his math homework and fines him 25 cents for each incorrect answer.
Today, John received \$7.5 after completing 50 problems.

How many problems did John answer correctly?

ID 3095

How many generations forward must you go in order to have more than five hundred ancestors?

ID 3096

A password consists of three digits, from 0 to 9, followed by a digit or a capital letter from an alphabet having 26 letters.
Repetition of digits is allowed.

Determine the number of different passwords that can be created.

ID 3103

How many of the first 100 integers are divisible by either 6 or 7 ?

ID 3104

For every birthday of John's life he puts as many dollars in a piggy bank as his age in months.
There are 1260 dollars in the bank.

How old is John?

ID 3106

Jim won a contest in which the prize was his weight in U.S. dimes.

If a dime weighs 2.7 grams and if Jim weighs 56.7 kilograms, how much money did he win?

[ 1 dime = 10 cents = \$0.1 ]

ID 3143

The price of a T-shirt on sale is \$19.99.
The store reduced the original price by 25%.

Estimate the original price of the T-shirt.

ID 3147

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 less?

ID 3157

How many years ago did you have more than four thousand ancestors?

Assume that the time lag between two generations is 25 years. Try to find the minimal possible value.

ID 3161

Mr. Smith can read 1 page in 2 minutes. His wife can read 2 pages in 3 minutes.

Reading two different books, how many minutes will it take them to read a total of 77 pages?

ID 3183

An analogue clock loses 9 minutes each hour.
If the clock is set correctly at noon, what time is shown when it reads the correct time for the first time again?

ID 3186

Twelve European teams enter a football tournament.
Each team plays one match against each of the other teams, with three points for a win, one point for a draw and none for a defeat.
The probability of a draw is 0.5.

What is the most likely score of a team?

ID 3203

Yellow Taxi Service charges \$1.50 for the first mile and \$.78 for each additional mile.

How far could I go for \$20 if I gave the driver a \$3.5 tip?

ID 3205

The product of 2 integers is 1200.

Find the smallest possible sum of these numbers.

ID 3306

An integer consists of 110 digits such that any consecutive 10 digits are different.

What is the sum of all digits?

ID 3331

There are 20 balls in the box. X of them are white.
When we add 10 white balls, the probability of picking a white ball doubles.

Find X.

ID 3367

There are four brothers in a family.
The sums of the ages of three of them are 40, 42, 44 and 48.

What is the age of the eldest brother?

ID 3373

Bill buys oranges at five for \$1 and sells at one for \$5.

How many oranges does he sell to make a profit of \$120?

ID 3375

It takes two painters 6 days to paint a house.
The older painter would only take 18 days to do the job on his own.

How many days would the younger painter take to paint the house on his own?

ID 3388

A girl is 12 years old.
She is three times older than her dog.

In how many years will she be twice as old as her dog?

ID 3417

Roman numerals are a numeral system of Ancient Rome based on letters of the alphabet.

For example, XCVII is 97 (100 – 10 + 7).

Which year is written below?

MDCCCLXXXVIII

ID 3459

I sold two cars and received thirty thousand dollars for each car.
I received 25% profit on one of the transactions and lost 25% on the other.

What is my net profit on the two transactions?

ID 3461

A 300-dollar stock loses \$50 of its value for a week.

What percent of increase will recover all of its lost value?

ID 3490

Find the odd one out.

ID 3643

Your boss has been told to give you a medal at the end of the day, for each of the seven days you work for him.

The medals are attached to a strip. Your boss can cut the strip to separate the medals, but he is very lazy and the strip is so strong that he can only cut one strip thickness at a time.

What is the minimum possible number of cuts he has to make?

ID 3670

Everything is half price in a restaurant.
Even more, each pizza receives an N% rebate, where N is the pizza number in the purchase.
How much do I pay for five pizzas that were originally priced at \$10.

ID 3687

Which figure completes the sequence?

ID 3711

Logic puzzle.

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

Stenvey-ehigt muins stixy-terhe is

ID 3730

If you rearrange the letters NAPDOL, you would have the name of a

ID 3749

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 3927

A dog chases a rabbit, which was initially 20 meters away.
For every 11 meters the rabbit runs, the dog runs 9 meters.

How far must the rabbit run to be 100 meters from the dog?

ID 3957

Which number goes next?

1, 8, 11, 18, 80, 81

ID 4047

I stacked five dice.

What is the maximum possible sum of the dots on the faces of the cubes visible from all sides?

ID 4088

How many words are there in the English language?

Guess by using your logical reasoning.

ID 4141

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

How many people were swimming?

ID 4276

Jim can eat a 15-inch pizza in half an hour.

How long will it take for Jim to eat a 12-inch pizza at the same rate?

ID 4309

The price of a computer after discount was \$992.

If the discount was 20%, what was the original sales price?

ID 4344

A man and his beloved wife carry a 20kg basket.

If the lady carries only 8kg, at what distance from the weight does she take the pole?

ID 4387

John and Mary, whose average annual income is \$110,000, have just moved from Richland to Poorland.
The average household income is \$100,000 in Poorland and \$200,000 in Richland.

What happens to people in the countries?

ID 4422

What is the total surface area of 28 identical cubes which together have a volume of 3,500 cubic units?

ID 4512

I composed the numbers from strips of paper.

Find the odd one out.

ID 4539

Jane pedaled downhill at 20 km/h and it took 2 hours to travel from a Swiss mountain village to another village.
The return trip took 5 hours.

Find the average speed of the return trip.

ID 4623

What is the word coiled inside this circle?

ID 4631

Which of the following is least like the others?

ID 4640

Anika solves 10 problems, 80% of them correctly, in 20 minutes.
James solves 12 problems, three-quarters of them correctly, in 15 minutes.
How much time do they need to correctly solve 100 problems?

ID 4662

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

ID 4670

A five-digit number is evenly divisible by 9.

If four of the five numbers are 1, 2, 3, and 4, what is the fifth digit?

ID 4682

If half of five pizzas costs \$30, what would a third of eight cost?

ID 4692

What is the smallest integer that can be written with two digits?

ID 4781

How much are 33 cacao bags (of 44kg each) worth, if 10kg costs \$55?

ID 4785

Five teams of 4 students each met in a competition.
Each student shakes the hands of all adversaries.

How many handshakes occur?

ID 4799

The community library fines 20 cents per overdue day of the first week and 50 cents per overdue day thereafter.

If Gerry paid \$9.80 for 2 books, how many days was the overdue?

ID 4880

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

ID 4955

What team do you join to get the greater amount of melon?

ID 5149

There are 2 matches.

What is the least number of matches that can be added to make 9?

ID 5170

Evguenia's birthday parties are always the same, and always boring. She gets seated at the table first. There are three other places set with named seating positions. Granddad always arrives next, and since he refuses to wear his glasses he always sits in a random position. Then her Aunt arrives, and if her place is free she takes it. Otherwise she sits in a random position. Then her mother arrives, and if her seat is taken she is grumpy all evening.

What is the probability that her mother gets to sit in her named seat?

The problem was suggested by Leslie Green

ID 5200

There are 3 different positive integers that have the same answer whether they’re added or multiplied together.

What is the largest number?

ID 5211

"My car uses 10 liters / 100 km and has a 70-liter tank.

The Village Garage sells fuel for \$1.40 per liter. It is just several meters from my house. Several garages outside the village sell fuel for \$1.36 per liter.

How far could the garage be so that it is worthwhile to drive to and back from the garage to refuel?"

ID 5215

Some forms of loans are more iniquitous than others. Find the loan method with the most extortionate rate.

(Definition: Iniquitous – grossly unfair and morally wrong)

NOTE: in some regions, Lenders are required to state the Annual Percentage Rate (APR) in order to make comparisons easier.

ID 5231

In a particular city it is illegal for those aged over 18 to consume children's chocolate drinks. Jack is walking home and drinking a chocolate drink. Sadly he is now 3 months too old to do so. When he sees a cop he therefore runs away and dumps the drink over a fence. The cop arrests him and charges him with arson. WHAT! Jack was wearing a green coat and the arsonist was seen wearing a green coat. At the police station the cops claim that only 2,000 people in this city of 100,000 people wear green coats. The odds of randomly finding him were therefore 2,000/100,000 making it 98% certain that he is the guilty party.

Using the evidence presented, what is the correct conclusion?

Author: Leslie Green

ID 5250

If Bob is exactly 9999 days old today, how old is he?

ID 5254

Would you rather work five days at \$120 per day or be paid \$20 the first day and have your salary double every day for a 5-day week?

ID 5323

At the bank, Gerry asks to exchange two \$100 bills for \$1, \$2, \$5, \$10, \$20, and \$50 bills so that he has at least one bill of each value and the number of bills is at a minimum.

How many bills does Gerry receive?

ID 5362

Gerry drives to his work 4 days per week and his office is 10 miles away from his home.
His car drives 40 miles with a gallon.

If gas was \$2.49 per gallon, how much would Gerry spend on gas in a month (4 weeks)?

ID 5437

Gerry writes 1.
He either adds or multiplies it by the next integer number. He does the same with the next number and so on. The last number in use is 5.

What is the largest result he can get?

ID 5452

There are 4 playing cards face up in a line on a table. Each of the cards has a different value. The cards need to be sorted so that the smallest value is on the left. There is only one action you can perform, namely interchanging the position of two cards (swapping them). You cannot move a card to an empty space.

What is the minimal number of swaps achievable on the worst possible arrangement of cards?

Author: Leslie Green

ID 5462

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 Russian computer scientist. His tests played an important role in the disciplines of cognitive psychology and cognitive science.

ID 5472

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

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 5527

There’s a tennis tournament with one hundred players.

How many matches does it take to determine a winner?

ID 5533

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 5542

The wages of 8 workers for a five-day week is \$ 6,000. What are the one day’s wages of 5 workers?

ID 5549

They said their names.

The girl said "My name is Taylor."
The boy said "My name is Taylor."
The dog said "Woof."
Only one of them lied and all the names are different.

Who told the truth?

ID 5555

Jane has 34 apples. Two apples can be traded for 1 mango, and each mango can be traded for either 4 apricots, or 3 pears, or 1 orange.

How many smoothies can Jane make, if each smoothie requires 1 apple, 2 mangos, 3 apricots, and 1 orange?

ID 5679

Olga was born in 1985 and her younger sister Evguenia was born in 1998.

Which statement is correct about the age difference of the two sisters?

ID 5705

In a tenth grade class, every three girls put their money together and buy a chocolate Easter Egg for each boy of the class and every four boys buy a chocolate Easter Egg for each girl.

If there are 21 pupils in the class, what is the largest possible number of Easter Eggs that will be bought in total?

ID 5725

The last day of January is Sunday.

What was the first day of the month?

ID 5738

My collection contains British, Russian and Swiss stamps.

Find the ratio of British to Swiss stamps, if the ratio of British to Russian stamps is 4 to 3, and the ratio of Russian to Swiss stamps is 2 to 3.

ID 5796

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 5802

Five rabbits bought a scale which is imprecise for small and large weights. It is OK for weights between 9 and 19 kg. The rabbits weigh themselves in pairs in every possible combination, resulting in the following :

10, 11, 12, 13, 14, 15, 15, 15, 15 and 16 kg.

How much do the five rabbits weigh all together?

ID 5804

In a chess tournament there are 10 players participating. Every player has to play with every other player. Players are granted one point (1) for a win, a half (1/2) point for a draw, and no points (0) for a loss toward their tournament score.

What is the average score for the players?

ID 5812

A car has accelerated from 0 to 144 km per hour in 10 seconds and traveled at the constant speed.

How much time does it take to drive 7 km?

ID 5956

Analyze the following statement as if it were true:

"HyperBrite cleans off 4x as much dirt as the nearest competitor."

What can you say with certainty?

Author: Leslie Green

ID 5969

Two identical airplanes (aeroplanes) set out on a vital mission. The lead plane is carrying a secret message which needs to be delivered by hand. Each plane has a full fuel tank and a 1000 mile range. The planes can transfer fuel in mid-air; this process loses no fuel and happens almost instantly.

How far can the lead plane get?
(Note that a plane with no fuel can still land safely.)

Author: Leslie Green

ID 6042

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

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 6131

Which number has letters in alphabetical order?

ID 6193

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 6283

Words can be tricky. The same word can have different meanings dependant on where it is used in a sentence, and can have different meanings even within the same sentence.

Am I being mean when I ask what the mean of the means means?

ID 6397

You meet a boy from a region of two cities: Truth City and Lies City. Truth City dwellers always tell the truth, and Lies City dwellers always lie.

If you want to know the direction to Truth City at a fork of two roads what question will make him direct you correctly?

ID 6462

A recruitment agency gets paid for each contractor they place, and they pass on 80% of the fee to the contractor.

But looking at it the other way around, starting from the contractor's fee, how much has the agency marked up the contractor's salary?

ID 6504

John has been driving for several hours in busy traffic and realises that most of the cars he has seen are different, neglecting color (colour).

What is the most reasonable explanation for this?

Author: Leslie Green

ID 6716

Here is a number sequence with a definite mathematical rule to move from one number to the next.

3,   7,   16,   43,   124

The tricky thing is that one number (not necessarily at the end) has been deleted from the sequence, but which number?

(Hint: This is just mathematics. It works in any language, not just English.)

ID 6746

Friday the 13th is considered an unlucky day in Western superstition.

What is the largest number of Friday the 13ths that can occur in a calendar year?

ID 6950

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 7095

The cards have a number or letter on one side and a color on the other side.

Every card that shows an odd number on one side has the color green on the other side.

How many cards do you need to flip to be sure that the rule is valid for all the cards?

An even number is an integer which is evenly divisible by 2 : 0, 2, 4, 6, 8, . . .

Odd numbers are not evenly divided by 2 : 1, 3, 5, 7, 9, . . .

ID 7173

You have a long gold chain and pay for your stay in a hotel by a link per day every morning. You stay eleven days in the hotel. You may take change in the form of links previously paid.

What is the least number of links you must open?

Inspired by: The USSR Problem Book by Shklarsky, Chentov, and Yaglom, Freeman, 1962.

ID 7297

Gerry uses a very original password that includes letters and spaces. The only information he gave to Jane was: "My password is out of date and I want to change it."

Based on the given information, guess how many letters the password has.

ID 7301

There is a barrel with no lid and some olive oil in it. Gerry tilts the barrel until the oil would barely touch the lip of the barrel. The bottom of the barrel is visible.

Gerry says: "This barrel of oil is more than half full."
Jane says: "It's less than half empty."

Who is correct?