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Aplusclick Olympiad Questions
Find the smallest positive integer that must be added to 2010 in order to . . .
Which gives the smallest answer?
The first person is 100 cm tall. Each subsequent person is 20% taller than the . . .
Find the hundreds digit (third digit from the right) of the product: 44444 x . . .
Which gives the largest answer?
How many 2-digit integers are there in which the sum of the digits is equal to . . .
How many digits are in the product of 2
^{101}
and 5
^{99}
?
Choose the answer without using a calculator. Which number is evenly . . .
How many sets of at least two consecutive positive integers have a sum of 15?
On this target, I scored exactly 80. How many shots did I fire?
In how many ways can you choose 4 of the first 8 positive integers so that no . . .
Which is the sum of all digits of the decimal representation of 5
^{16}
. . .
The sum of the digits of a two-digit number X is Y. The sum of the digits . . .
Which gives the largest answer?
What is the largest sum of two integers such that their product is 787?
The date July 31, 1370 in MM/DD/YYYY format is a palindrome that may be read . . .
How many three-digit numbers have exactly five divisors including 1 and itself?
An hour ago, I notched up 78987 kilometers on my odometer. The number is . . .
Make two fractions with all the digits from 0 to 9. Use each digit once. They . . .
Make 33 by using three 3s and any math operators. How many times do you use . . .
The sum of two prime numbers is equal to 888. There are several options. We . . .
Find the smallest positive integer that must be added to 2010 in order to . . .
Find the last three digits of the product: 44444 x 99999
How many 2-digit integers are there in which the sum of the digits is equal to . . .
How many digits are in the product of 2
^{101}
and 5
^{99}
?
Choose the answer without using a calculator. Which number is evenly . . .
On this target, I scored exactly 90. How many shots did I fire?
Pairs of primes separated by a single number are called prime pairs. Examples . . .
How many positive integer numbers are twice the sum of their digits?
Find the last 3 digits of the sum of 1 + 11 + 111 + . . . + 111 . . . 111, . . .
Three integer numbers yield the same answer whether they are added or . . .
Which is not correct? Remember that 3! = 1 x 2 x 3
If you wrote all the whole numbers from 1 through 1000, how many times would . . .
With a 1 after a nine-digit number, it is the same as a 1 before it. Find . . .
I multiply the two page numbers and get 6162. What is the right-hand page . . .
What are the two last digits of the result? 1999999991 x 2000000009
How many sets of three consecutive integers whose product is equal to their sum . . .
Write natural numbers 1, 2, . . .100 in a row so that the difference between . . .
Which number is smaller than the sum of its divisors other than 1 and the . . .
How many digits are there in the number 625
^{10}
? Please don't use a . . .
If the sum of 999 positive integers is equal to 1000 what is their product?
What gives the largest result?
The product of two integers is 1000. Neither of the numbers contains a zero. . . .
Savin's problem: Using each of the digits 1,2,3, and 4 twice, write out an . . .
What number is largest?
What gives the smallest result? Here we write 0.333 . . . as notation for . . .
The product of 99 integers is 99. What is the largest possible value the sum . . .
What is the sum of the first 100 prime numbers? A prime number is a natural . . .
Use four 9's and any math signs to make 100. How many sign '+' did you use?
Solve this. F = (a - x) (b - x) (c - x) . . . (z - x)
0.999 . . . means infinitely repeating decimals. What is the largest result?
What number added to itself three times is equal to 72?
A magic square is an arrangement of integers, in a square grid, where the . . .
Leslie Green asks: What is the next number in the sequence? 0, 3, 1, 4, . . .
Find two numbers so that their sum, product and the result of division are the . . .
Use three 5's and any math signs to make 19. How many '+' signs did you use?
Find the sum of all the elements of this finite geometric sequence: 1, 2, 4, . . .
The last digit of the number 3
^{33}
is:
A perfect cube is an integer whose cube root is an integer. For example, 64 . . .
Eugenia used 192 digits to number the pages in her diary. How many pages . . .
How many digits are in the result of the expression? 1001
^{11}
How many 2-digit numbers have a tens digit that is smaller than the units digit?
Which of the following gives the biggest answer?
What is the smallest integer that is 4 times the sum of its digits?
Choose the answer without using a calculator. I multiply together the . . .
Find the last digits of the product. (7 x 5 x 4 x 5 x 3 x 1)
^{33}
A square game board begins with a dark square alternating with light squares. . . .
What is the largest product of positive integers that add up to 17?
F = (x-a)(x-b)(x-c) . . . (x-x)(x-y)(x-z) Find F.
A4321 is a five-digit number in which A is a digit and the number is evenly . . .
Find the sum of all the elements of this finite geometric sequence: 1, 2, 4, . . .
The last digit of the number 4
^{44}
is:
A perfect cube is an integer whose cube root is an integer. For example, 64 . . .
Anna used 189 digits to number the pages in her diary. How many pages does . . .
How many 2-digit numbers have a tens digit that is greater than the units digit?
Choose the answer without using a calculator. I multiply together the . . .
Divide 77 into three parts so that one is 150 percent of each of the other two. . . .
Engineers at a race company make three discoveries. The first invention saves . . .
A car starts traveling at an initial speed of 120 km per hour (kmph), the . . .
Which number between 40 and 50 can be expressed both as the sum of two . . .
There are 190 coconuts in a basket. Sailors one after another take out half of . . .
Mike’s age, M, is equal to the sum of the ages of his four children. His age N . . .
The Smith family consists of parents, children, and animals. Some of them are . . .
In a city, sixty percent of the men are married to eighty percent of the women. . . .
"A coach leaves London for York and another at the same moment leaves York for . . .
Mr. Rapid always starts driving on a road at exactly 7:00 a.m. If he drives on . . .
How many "yes or no" questions are needed to guess any 5-digit code?
A series of 10 books were published at two-year intervals. The sum of the . . .
The product and sum of two positive integers X and Y are added together. The . . .
Find x.
X + XY + Y = 34 Find all positive integer solutions of the equation, for which . . .
Which gives the smallest answer if X and Y are integers, X is greater than . . .
How many pairs of prime numbers add up to 101?
0.123123123123123 . . . . What fraction is it?
If the sum of two numbers is 9 and their difference is 11, what is their . . .
A grocery store sells Brazilian cacao in 15-kg bags and Ecuadorian cacao in . . .
A cube is painted on the outside and then divided into one-unit cubes. The . . .
Which of the following is equal to fourteen divided by nine?
Two trains start at the same time, one from Zurich to Lausanne, the other from . . .
Which step is the flaw in the proof?
Find two positive integers that don't end in zero, and have a product of . . .
How many of the letters in the Russian alphabet have more than one line of . . .
The letter 'A' is symmetrical. A symmetrical figure can be folded in half and . . .
For which letter did I use the smallest amount of green paint?
Each square is 1 square unit. What is the area of the colored triangle?
Which shape has the largest shaded region in terms of area?
The figure shows a regular hexagon. What is the fraction of the area of the . . .
I strike a pool ball from corner A of the rectangular billiard table at an . . .
The squares have side lengths of 2 and 4. Find the area of the colored . . .
The figure shows a regular octagon. What is the area of the colored part as . . .
The diagram illustrates a row of three squares formed by matches. How many . . .
The picture shows two identical squares with sides that have a length of 1 . . .
Two lines and two diagonals are drawn through the center of the rectangle. . . .
How many equilateral triangles can you create using six identical matches? . . .
A boy cuts a cardboard circle and only cuts 5 straight lines. He does not . . .
How many planes of symmetry does a cube have?
How many boxes measuring 0.1m x 0.1m x 6.9m can be packed into a container . . .
A boy stacked colored cubes in a square pyramid like the one shown here. The . . .
A six-pointed regular star consists of two areas. What is the ratio of the . . .
The figure shows a red equilateral triangle inscribed within another . . .
There are 2 identical circles. Circle A remains fixed, while Circle B makes 1 . . .
What is the maximum number of squares you can make using twelve identical . . .
Divide the analog watch face with two straight lines so that the sums of the . . .
Twenty matchsticks form five squares (one 3x3 and four 1x1). How many . . .
Which of the nets can be folded into a box with a red ribbon printed . . .
The blocks of ice are of the same height and depth. Which assembly melts . . .
A ladder leans against a vertical wall. The top of the ladder is 4m above the . . .
All inner lines connect the corners of the big square and the midpoints of the . . .
Among the following shapes of equal area, which has the smallest perimeter?
The sizes of the sealed bottle with water are shown in the figure. Find the . . .
How many equilateral triangles can you make using six identical line segments?
In a 3 x 3 grid, there are 8 lines that contain at least 3 points. How many . . .
How many triangles are there?
The following pattern is cut and folded to a square-based pyramid. What size . . .
I fold a square piece of paper in half four times without unfolding, making an . . .
Every face of a cube has at least one white edge. What is the smallest . . .
How many squares can be formed by joining four of these points on the . . .
How many more lines must I draw to make a shape that has a line of symmetry? . . .
Which of these parts has the smallest area?
What is the maximum number of possible points of intersection of N different . . .
The diameter of one hair is 0.2 mm. Estimate the diameter of a plait of 1000 . . .
I want to place together five identical shapes without overlapping them to form . . .
Compare areas F and G
The left picture shows nine dots arranged in a 3 x 3 square. The dots are . . .
What is the sum of the marked angles?
The picture shows six equilateral triangles. The sides of the triangles are . . .
The shaded rhombus is formed by joining vertices of the square to the midpoints . . .
Which of these diagrams could be drawn without taking the pen off the page and . . .
The diagram shows 15 billiard balls that fit exactly inside a triangular rack. . . .
Fifteen billiard balls perfectly fit into a triangular rack. What is the . . .
What is the smallest number of segments that needs to be moved so that the . . .
Which of these diagrams could be drawn completely without lifting the pen off . . .
The picture shows the areas of three rectangles. What is the area of the . . .
This shape was formed by removing a small cube from a big cube. The volume of . . .
I want to cut round bread into eight equal pieces. What is the smallest . . .
A girl wants to cut the paper into several equal pieces of the same shape, and . . .
How many colored four-unit shapes can be placed inside the 6x6 square without . . .
Two triangles form seven separate regions. What is the greatest number of . . .
What fraction of the large equilateral triangle is colored?
Four matchsticks form a square. How many non-overlapping squares can be . . .
There are six ways to travel from point S to point F on a small cube if only . . .
The game Battleship (Battleships or Sea Battle) is a guessing game played by . . .
Seven squares with side length of 1, 2, 2, 2, 3, 4, and 5 units can be fitted . . .
I want to cut this shape into four pieces all of precisely the same size and . . .
How many circles are needed to separate each star from all of the others?
I would like to cut the shape into the fewest possible pieces that will fit . . .
The colored figure in the picture consists of isosceles right triangles. . . .
A, B, and C are squares with sides of length 1; D, E, and F are isosceles . . .
What is the maximum number of pieces that an apple can be divided into with . . .
I arrange 10 points so that 3 lines each go through 4 points. I would like to . . .
Find the radius of the circle.
In a city, there were seven bridges. There was a tradition that a newly . . .
Four matchsticks form a square. How many non-overlapping squares can be . . .
A sphere fits inside a cube. The maximum possible ratio of the volume of the . . .
I want to cut a wooden cube that is five inches on each side into 125 one-inch . . .
I arranged twelve one-inch wooden sticks in a polygon with an area of 6 square . . .
Find the angle between two diagonals drawn on two faces of the cube.
What line divides the green polygon into two parts of equal area?
How many apples can I place, such that the distance from every apple to every . . .
The letter 'A' is symmetrical. A symmetrical figure can be folded in half and . . .
For which letter did I use the greatest amount of green paint?
Which shape has the largest white region in terms of area?
Calculate the area of the shape in small squares.
The diagram illustrates a row of three squares formed by matches. How many . . .
A boy stacked colored cubes in a square pyramid like the one shown here. The . . .
The figure shows a red equilateral triangle inscribed within another . . .
The blocks of ice are of the same height. Which assembly melts slowest?
Which of these parts has the largest area?
I need 1 + 4 + 9 + 16 + 25 = 55 cubes to build a pyramid with a height of 5 . . .
A bug walks from corner A of a room to corner B by only moving along the walls. . . .
I want to place N cubes so that each cube touches every other one. What is . . .
What is the volume of the second glass compared to the first one?
The Babylonians used a base 60 number system. What shape inspired them to . . .
Connect N points on the circumference of a circle. What is the largest number . . .
I take a map of the city where I live and lay it on my table. There is a . . .
Which is the odd one out?
I connected the midpoints of a polygon and constructed a new polygon that was a . . .
A pyramid and a tetrahedron with edges of the same length are glued together on . . .
Cut the shape into two pieces and create a square from them. How many small . . .
I need 1 + 9 + 25 = 35 cubes to build a pyramid with a height of 3 cubes. . . .
Find the missing part.
If a square is four and a triangle is three, how many is a regular star?
Inspired by Boris Kordemsky. Four Knights problem: Cut the chessboard into . . .
Squares 1, 2 and 3 have sides of length 1, 2 and 3 units, respectively. What . . .
What is the absolute difference between the largest and smallest possible . . .
A square with a side length 20 has two vertices on the circle, and one side . . .
What is the difference between the red area and the blue area if the numbers . . .
How many 1x1 squares fit into the large square with the side length 4.8? . . .
The picture shows three squares with the side lengths of 10, 8, and 4 cm. What . . .
The figure shows adjacent squares. Find the sum of angles X and Y.
The hypotenuse of a right triangle is 6, and the length of one leg is 2 units . . .
How many lines can be drawn in a plane so that they are equidistant from 3 . . .
I have 33 coins. What is the minimum number of coins I need in order to make . . .
What is the maximum number of trees that can be planted, not closer than 3 . . .
Which triangle has the greatest area?
Two perpendicular lines form four segments with lengths a, b, c, and d. . . .
Three overlapping squares form 5 squares including themselves in the picture. . . .
The size of an NBA basketball court is about 29 by 16 meters. How many . . .
How many pentagons are there?
The year was read the same the correct way up as upside down. When was the . . .
What is the maximum number of sections into which a pancake may be divided by . . .
For which shape did I use more wood?
The numbers show the areas of corresponding triangles. What is the area of . . .
How many squares one inch on a side can be fitted into a circle with a . . .
An arrangement is formed by laying nine colored squares of the same size one . . .
I divided a 3 x 4 square into 6 squares. What is the smallest number of . . .
I want to divide this shape into four congruent pieces - all of precisely the . . .
Divide the square into four equal shapes, so that each shape includes a circle. . . .
What is the largest number of straight lines you can draw through 9 points, so . . .
What is the difference between the red area and the blue area if the numbers . . .
Find the area of the colored rectangle.
Britain’s greatest inventor of mathematical puzzles Henry Ernest Dudeney asked . . .
What is the minimum number of matches that must be moved in order to obtain two . . .
All sides of the white cross are the same. What percentage of the square is . . .
What is the largest distance if the angle B is right?
Marek, the pan-dimensional super being, has arbitrarily defined his current . . .
What is the minimum number of matches that must be moved in order to obtain . . .
A large rectangle of perimeter 44 is divided into 10 congruent rectangles. . . .
How many squares of any size are there in the picture?
How many diagonals can I draw in an octagon?
How many stars will be in the fourth line of the pattern?
Bob is rolling two dice and adding the numbers on the top faces. What sum is . . .
The average of eleven numbers is 9 and the average of another set of nine . . .
Fifteen numbers have an average of 15. Five of these numbers have an average . . .
Three boxes contain two coins each. One contains two nickels, one contains . . .
If two dice are rolled 72 times, how many times is the sum of the two top . . .
I roll two dice. What is the probability that the second number is greater . . .
Five students put their sandwiches into five paper bags. The bags are . . .
Four kinds of apples are combined in a box. I select apples from the box . . .
By drawing two marks on a wooden ruler, we can measure 1, 2, 3, 4, 5 and 6 . . .
John is sick 6 days per year. The probability of being sick on a Saturday or a . . .
A boy begins walking from his starting point. Each hour, he either walks one . . .
What is the units digit of 1! + 2! + 3! + ... + 2011!? 4! means 1 x 2 x 3 x 4
Two princes and two princesses are ready to marry. Everybody independently . . .
A 4-character password uses exactly two different digits. Each digit can be 0, . . .
After a rodeo, four cowboys have a meeting in a saloon. Each cowboy has only . . .
Two dice are thrown. You can see all 12 numbers except 2 faces that are on the . . .
After a gun is fired in a saloon, 75% of the cowboys have a wounded ear, 80% . . .
If we set out by ranks of 10, we will be one short. We will also be one short . . .
Which shape cannot be folded to form an open box?
Two dice are thrown. Two numbers are multiplied. What product of numbers . . .
Two cards are randomly chosen. Two numbers are added. What sum of numbers . . .
What is the average of the smaller of three random numbers from 0 to 1?
How many seconds were in 2012?
Each of four children chose one of these cards. They multiplied the chosen . . .
Bob the plumber has 10 pockets and 60 nuts. He wants to put the nuts in all . . .
Forty non-zero positive numbers are written in a row. The average of the . . .
Make 727 by using three 7s. You can use any math operator that you would . . .
Place the number tiles in the squares so that no two consecutive numbers are . . .
Anna (A), Bill (B), Cindy (C), and Daniel (D) work on a project. (1) . . .
How many different cubes can I make by using six different colors such that . . .
There is a legend that a stork brings babies to a village. All parents . . .
I arranged eight wooden sticks in the shape of a fish. What is the minimum . . .
An entrepreneur wants to hire the best person for a position. He makes a . . .
On average there are 100,000 strands of hair on a person's head. Hair grows . . .
Logic puzzle: Counting down from 100 by one, which number comes next?
A group of kids with dogs go for a walk. There are 49 feet and heads . . .
How many seconds are there in a year?
What is the logic behind? What is the correct answer?
A two-digit integer is 4.5 times larger than the same number read from right to . . .
One word on this page is spelt incorrectly. How many letters are there in . . .
Bob is rolling two dice and will subtract the second number from the first . . .
The average of twelve numbers is 8 and the average of another set of eight . . .
Fifteen numbers have an average of 10. Five of these numbers have an average . . .
If two dice are rolled 72 times, how many times is the sum of the two top . . .
I roll two dice. What is the probability that the two numbers are equal?
Four kinds of apples are combined in a box. I select apples from the box . . .
John is sick 12 days per year. The probability of being sick on a Saturday or . . .
Bob the plumber has 8 pockets and 40 nuts. He wants to put the nuts in all . . .
A palindrome is a word, phrase, or sequence that reads the same backwards as . . .
What is heavier than a cumulus cloud, which is about 1 cubic kilometer in . . .
Eight bugs are at the eight corners of an equilateral cube. Each bug randomly . . .
Logic question. What is the easiest way to make the following equation . . .
If 2 salesmen can sell three luxury cars in 4 days, how many luxury cars can . . .
How many coins must you move to form two infinite lines, each with exactly five . . .
Order the shape by weight from lightest to heaviest.
Order the shape by weight from lightest to heaviest.
A chess queen attacks all squares along its path horizontally, vertically and . . .
We want to merge 4 companies into one large company. How many ways are there . . .
A bus carrying 5 tourists travels to Dogland. Every tourist has a dog. Every . . .
Find the sum of the series: 1/3 + 1/9 + 1/27 + 1/81 + . . .
Alex and Bill both have some money. Alex is short of two dollars and Bill of . . .
A surgeon has two pairs of surgical gloves. What is the maximum number of . . .
What is the average of the largest of N random numbers from 0 to 1?
I want to find the smallest number divisible by 225 that consists of ones and . . .
Alex(A), Beatrice (B), and Craig (C) work on a project. (1) Together, A and . . .
Place the cards into two boxes so that the probability of randomly drawing a . . .
Arrange nine numbers in a circle so that the difference between neighboring . . .
I ask you to pick a number from 1 to 100. I then ask you, “Is the number . . .
This is a standard set of dominoes. Choose 2 dominoes at random. What is . . .
You can throw as many darts as necessary at the board shown in the picture. . . .
Which year has had the greatest number of Roman numerals in it?
Which result ends in exactly seven zeroes. Remember: N! = 1 x 2 x . . . x N
You roll two dice. Estimate the expected value on the highest valued die?
After a test of a code, John detected 2 errors and Mary discovered 3 errors in . . .
John and I have a glass of milk. He drinks half of it and then I drink half of . . .
Five students Anna, Bill, Craig, Daniel, and Eugene commute by bus. Every . . .
Find the product of 111,111,111 x 111,111,111
The amount of water flowing into a tank doubles every minute. The tank is full . . .
If the probability of observing a white car in 10 minutes on a motorway is . . .
There are 5 children in a boat. Four of them do one of the activities below. . . .
The sum of the integers from 1 to 2,000 inclusive is 2,001,000. What is the . . .
Jane picks a random integer between 1 and 5 (inclusive) and Gerry does the . . .
How many 9s are there in the result of the multiplication: 12345 x 99999 ? . . .
How many 3x3 squares are there on a chessboard?
95.8% of James' classmates have different numbers of hairs than he has. How . . .
How many different bracelets can you make from four beads?
The product of 20 positive integers is 56. What is the smallest possible sum . . .
James the Mathematician wants to find a partner for a serious relationship. He . . .
The sum of 11 consecutive integer numbers is 11. What is the largest number?
The sum of 55 consecutive integer numbers is 5555. What is the largest . . .
Which number goes next? 1 1 2 3 5
I got a total of 120 by using five zeros and any mathematical operators. How . . .
I throw a coin on a chessboard. The diameter of the coin is a half of the side . . .
Coin landing on its edge I flip a fair Swiss franc* and it falls in . . .
I roll two dice, one with the left hand and one with the right. If the left . . .
What is the sum of dots that are not visible from the current direction, but . . .
Jane was a naughty little girl. When she used to play 2-dice games with her . . .
Gerry tosses 2 coins and Jane tosses 3 coins. What is the probability that . . .
A team of two geeks, Jane and Gerry, independently answers true-or-false . . .
Anton, the highest IQ house ant on the planet, is taking his regular nocturnal . . .
Martin, the mathematical mole, has dug an extensive network of underground . . .
Marek, the pan-dimensional super being, has arbitrarily defined his current . . .
Twenty Knights sit around the Round Table in the following order: 1. King . . .
An escaped criminal has stolen a spaceship, and has just instantaneously jumped . . .
Despite advice to the contrary from his friends and parents, Timmy has decided . . .
What are the odds of getting at least two tails in a row if you flip a dime . . .
One hundred workers complete a project in 100 working days. Adding any . . .
Each of four children has a photo. Anna and Bill's photos show water. Only . . .
How many letters are there in the correct answer to this question?
There are 20 students in a class. 12 students have red stars and 8 students . . .
Tom writes a total of forty words on five blank cards. He writes nine words . . .
Brad has as many brothers as sisters. How many more brothers than sisters . . .
The total weight of Bob and his sister Anna is 155 kilograms. Bob's weight is 2 . . .
If you write all numbers from 0 to 109, which digit (numeral) will you write . . .
Ten men met at a conference. Each man shook hands with each of the other men . . .
The product of three consecutive whole numbers is 999,900. What is the . . .
Three boys, A, B, and C, are at the corners of a rectangular field. At which . . .
Eugenia, the magician, receives a 50% discount every time she asks for the . . .
Four friends tried to guess the number of sheep in a flock. Alex guessed 21, . . .
How many cubes will balance one sphere?
Alex needs six tacks to fix two rectangular pictures because he can overlap the . . .
The picture shows the first five notes of the tune 'We Wish You A Merry . . .
There is a set of 10 numbers. Five numbers are selected from the set and added . . .
John's dad pays him 80 cents for each correct answer he provides in his math . . .
Five students put their sandwiches into five paper bags. The bags are randomly . . .
Eugenia's grandmother bought a new car for $55,000 in 1970. The car . . .
I want to put exactly 4 liters of milk into a large tub with a capacity of . . .
How many generations forward must you go in order to have more than one . . .
In the first week John made $1. He made 5 times more than the previous week . . .
Anna's income is seven-eighths that of Beatrice. Anna's expenses are . . .
Anna wants to score exactly 33 points. The ducks give different points. How . . .
The diagram shows some of the results of a six-person contest. There are two . . .
How many times do the hour and the minute hands form a 90-degree angle in the . . .
John read a 165-page book in 11 days. Every day, he read 1 page more than the . . .
The first six numbers in a sequence are shown on the right. What is the 66th . . .
The number 99! is very big. How many zeros are there at the end of the . . .
What is the sum of 99 consecutive integers, if a third of them are negative . . .
I arrange five marbles randomly in a ring. There are two green and three . . .
A girl was born in the 20th century. Take away from her year of birth the sum . . .
Mr. Smith can read 1 page in 2 minutes. His wife can read 2 pages in 1 minute. . . .
The twins are the same height. They place four identical blocks as shown in . . .
How many two-digit integers are there in which the sum of the digits is equal . . .
Ten years ago, Bob was three times as old as Anna. Today, he is twice as old . . .
Statement 1: There are 3 animals in a room. Statement 2: All of the animals in . . .
How many straight lines are needed to separate each star from all the others?
Two gears, one with 11 teeth and the other one with 18 teeth, have teeth marked . . .
1. At least 1 of these 6 statements is false 2. At least 2 of these 6 . . .
You take half of the syrup and mix it with the water, and then take the same . . .
The matchsticks make a spiral that goes clockwise. How many matchsticks do I . . .
The figure shows a triangle made of discs. I want to move the discs and turn . . .
Two rectangles enclose five regions. Find 2 figures that can form the . . .
In-Out Machine transforms 111121 into 100. The same machine transforms 121244 . . .
An analog clock loses 15 minutes each hour. If the clock is set correctly at . . .
What is the largest number you can write with just two different digits?
Sixteen European teams enter a football tournament. Each team plays one . . .
A password consists of five digits, 0-9. How many passwords are there that . . .
The product of 2 integers is 1000. Find the smallest possible sum of these . . .
What is the condition for the smallest ten-digit integer that has only two . . .
A lady, attempting to avoid revealing her real age to her husband, says: I'm . . .
A dozen balls cost you $40. You get every fifth ball for free. How many . . .
The pages of a book are consecutively numbered from 1 through 999. How many . . .
The addition shown here has 21 terms and the last element consists of 21 9's. . . .
There is a total of 6 squares whose vertices are points on the rectangular 3 x . . .
I put $990 into 10 envelopes. I try to compose all possible whole amounts . . .
Alex has bills of different dollar values. There are five times as many ones . . .
On January 1st, Anna and Bill have $100 each. Each month Anna saves $10 more . . .
Four painters can complete a painting job in 20 days. 12 more painters join . . .
An integer consists of 2010 digits such that any consecutive 10 digits are . . .
Twelve couples met at a party. Each person shook the hand of each of the . . .
The time on a digital clock reads 9:43. What is the shortest length of time, . . .
There are a number of apples, all of different weights. The 10 lightest apples . . .
There are four brothers in a family. The sums of the ages of three of them are . . .
In how many ways can the name ALEX be spelt out, using adjacent letters of the . . .
What number should replace the question mark?
What number should replace the question mark?
Find the missing figure.
Which shape fits in the missing space to complete the pattern?
Three children and two adults want to cross a river. Their boat can carry . . .
Which of these diagrams could be drawn without taking the pen off the page and . . .
I wrote all the numbers from 0 to 999. Which digit did I write less than the . . .
How many different ways are there to go from A to B?
Each of these seven cells contains one number from 1 to 7, using all seven . . .
Two apples and two peppers have the same weight as three eggs. Six eggs and . . .
There are eight buckets; four of them are filled with water. What is the . . .
I enclosed 9 apple trees using a large square fence. What is the smallest . . .
A group of gentlemen visited a produce shop. Each gentleman bought the same . . .
A number is said to be perfect if it is equal to the sum of its divisors. . . .
The matchsticks make four small squares and one big square. How many . . .
Multiply all positive two-digit numbers. How many zeros are there at the end . . .
Which pair of shapes is not like the others?
A banker forgets which key fits in which of three keyholes. What is the . . .
You have four piles: three piles with real coins and one pile with fake coins. . . .
How many times do the two hands of a clock point in the same direction between . . .
How many zeros are there at the end of 100! ?
Use each digit, 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, exactly once to form two . . .
Logic puzzle. There are three mothers and three daughters in a group of . . .
Tricky Equation Puzzle: the equation below is wrong: 102 - 99 = 1 Which . . .
Anna ran in the north direction at a speed of 8 km/h, Bobby ran east at a speed . . .
I must balance any whole number load from 1kg to 40kg using these four weights . . .
How many different lines that extend to infinity in both directions can you . . .
A kitten has a 50/50 chance to be male or female. My cat just delivered two . . .
If each row and each column of the square must contain exactly one triangle, . . .
2889 digits are used to number the pages of a book beginning at page 1. How . . .
Find the next letter in the sequence.
A bee crawls along the sides of the honeycomb hexagons. It has moved from . . .
Twenty-two performers have numbers 1 to 22. A couple finds that their numbers . . .
How many three-digit numbers containing only even digits are divisible by 9?
What is the largest digit in the product of 11111111 x 11111111 ?
I would like to plant 10 trees in 5 rows of X trees. What is the largest . . .
A farmer puts several pigs into three pens. None of the pens is empty. All . . .
How old is the eldest of these four sisters if the product of their ages is 792?
Thinking outside the box: 52 - 28 = 4 Which digit has to be moved to . . .
Large individual letters are differently priced. The letters in the word . . .
Which number comes next? 2, 12, 1112, 3112, . . . .
If a hen and a half lay one half of an egg in two days and a half, how many . . .
I want to measure exactly six minutes from the moment I touch an hourglass, . . .
Logic puzzle: a secret door. A man approached the door of a secret . . .
Bill (B), Cindy (C), and Daniel (D) work on a project. (1) Together, B and C . . .
Logic riddle In a house, there are three switches on the ground floor for . . .
Logic riddle This occurs once in every second, once in every hour, and twice . . .
A lot of money is in a box. None or just one inscription on the boxes is . . .
I took several pieces of fruit from the bowls. All of them are cherries . . .
Use all the digits from one to nine and any combination of plus signs and minus . . .
One hundred soldiers form a 10 x 10 square. From every column, the tallest . . .
Find the odd one out.
What is the next letter in this series?
What is the largeest number of matchsticks I need to remove to make 10?
A donkey must transport 900 carrots to the market, which is 300 miles away. . . .
A magician placed 3 bowls of fruit in 3 closed boxes and 10 people tried to . . .
It takes exactly 1 hour to burn a rope when I light one of its ends. The rate . . .
Neglecting the seconds hand, how many times do a clock's hands overlap in a day?
By using 1 2 3 4 once each and any arithmetical operations +, -, x, and /, what . . .
Logic puzzle: What happens once in a minute, twice in a week, and once in a . . .
Which number should replace the question mark? 8 1 6 3 4 5 2 7 0 ?
John is 33 years, 33 months, 33 weeks, 33 days, and 33 hours old. How old is . . .
How many steps are required to break the Swiss chocolate bar into 1 x 1 pieces?
Anna, Bill, Cindy, and David show their photos. Each of four children has a . . .
Brad has as many brothers as sisters. What is the largest number?
The total weight of Bob and his sister Anna is 151 kilograms. Bob's weight is 1 . . .
Eleven men met at a conference. Each man shook hands with each of the other . . .
The sum of three consecutive whole numbers is 999900. What is the smallest . . .
Eugenia, the magician, receives a 50% discount every time she asks for the . . .
Alex needs six tacks to fix two rectangular pictures because he can overlap the . . .
There is a set of 10 numbers. Five numbers are selected from the set and . . .
John's dad pays him 70 cents for each correct answer he provides in his math . . .
John's dad pays him 75 cents for each correct answer he provides in his math . . .
How many generations forward must you go in order to have more than five . . .
In the first week John made $1. He made 4 times more than the previous week if . . .
Anna's income is seven-eighths that of Beatrice. Anna's expenses are . . .
I arrange five marbles randomly in a ring. There are two green and three . . .
Mr. Smith can read 1 page in 2 minutes. His wife can read 2 pages in 3 minutes. . . .
How many two-digit integers are there in which the sum of the digits is equal . . .
Twenty years ago, Bob was four times as old as Anna. Today, he is twice as old . . .
An analogue clock loses 9 minutes each hour. If the clock is set correctly at . . .
Twelve European teams enter a football tournament. Each team plays one match . . .
Twelve European teams enter a football tournament. Each team plays one match . . .
The product of 2 integers is 1200. Find the smallest possible sum of these . . .
A dozen balls cost you $50. You get every fifth ball for free. How many . . .
The pages of a book are consecutively numbered from 1 through 999. How many . . .
On January 1st, Anna and Bill have $55 each. Each month Anna saves $5 more . . .
An integer consists of 110 digits such that any consecutive 10 digits are . . .
The time on a digital clock reads 9:43. What is the shortest length of time, . . .
There are a number of apples, all of different weights. The 10 lightest apples . . .
There are four brothers in a family. The sums of the ages of three of them are . . .
A number is said to be perfect if it is equal to the sum of its proper . . .
Multiply all positive numbers below 33. How many zeros are there at the end . . .
Tricky Equation Puzzle: the equation below is wrong: 12 + 3 = 4 Which . . .
Anna ran in the north direction at a speed of 3 miles per hour, Bobby ran west . . .
Logic puzzle: a secret door. A man approached the door of a secret . . .
Find the odd one out.
What is the letter, which goes before O?
The figure shows a triangle made of discs. I want to move two discs and turn . . .
If I delete a letter in a word, then only one is left. Find the word.
Adding a letter to a word makes it odd. What is the word?
What is half of two plus two minus two? How many possible answers are there . . .
Kevin cleans rooms in a student hostel; he earns twice as much for cleaning a . . .
Logic riddle: In a house, there are three switches on the ground floor and a . . .
The five pieces of chain shown must be joined into a long chain. How many . . .
Which direction is the London coach going?
What is the next number in the following sequence? 1 11 101 111 ?
There is only one correct answer to the question below. Which answer is . . .
After a three-hour drive, I stopped my car in front of a wall with three doors: . . .
A four-letter word can be written forward, backward or upside down while . . .
What is half of 8?
Divide the circles into two disjoint groups so that the sums of the numbers in . . .
Anna, Beatrice, and Cindy run a 2000-meter race. All of them run at a . . .
Your boss has been told to give you a medal at the end of the day, for each of . . .
Which figure completes the sequence?
Is it legal for a man in Montana to dance with his widow's sister at her . . .
If you rearrange the letters NAMELESS, you would have the name of a
Logic puzzle. Only the first and last letters of the words below are in their . . .
"Three sailors come across a pile of coconuts. The first sailor takes half of . . .
I take half of the coconuts plus a coconut. What percentage of coconuts is . . .
I want to measure exactly six minutes using only a five-minute hourglass and a . . .
How many months have 30 days?
Logic puzzle. A word for a family member is the same spelled forward and . . .
United we stand, divided we fall. How many sets of antonyms are there . . .
Can you predict the score of any match before it begins? What is the score . . .
Mount Everest is the Earth's highest mountain with a peak at 8,848 meters . . .
An Honesty shop sells the first candy for 1 Swiss franc and each next candy for . . .
If you rearrange the letters NAPDOL, you would have the name of a
The numbers are the total of the values of the symbols within each column and . . .
There are 12 people in a village. They consume 12 coconuts altogether. Each . . .
Vladimir Arnold (1937-2010), one of the greatest 20th century Russian . . .
1 gives 2 2 gives 6 3 gives 12 4 gives 20 What does 10 give?
A committee consists of 7 people. The committee keeps an important object in a . . .
Thinking outside the box: Which statement is correct?
Thinking outside the box. Solve this:
The sum of consecutive integers is 10. Find the smallest of the numbers.
Which number goes next? 1 3 6 10 ?
Which symbol goes next?
Which number goes next? 1, 8, 11, 18, 80, 81
On an island, three-quarters of the men are married to four-fifths of the . . .
I stacked five dice. What is the maximum possible sum of the dots on the . . .
Five pirates capture some treasure. They divide the coins and find that there . . .
The rear tires of a car wear out after 40,000 miles, while the front tires wear . . .
When two non-zero integers are added, multiplied, divided, or subtracted, I can . . .
Find the logic: 12345678 rarr; 4 234567 rarr; 2 . . .
How many uninteresting numbers exist? The question is based on the . . .
Len's number is 31. Jim's number is 32. Sam's number is 33. Which number . . .
Once upon a time, there were three little pigs - ages 2, 4, and 6 months. If . . .
"This is a capital letter of the alphabet that's been folded just once. Which . . .
I multiply the ages of three kids and get 48. If I add their ages, what is . . .
Two trains are 1 kilometer apart on a single track railway line. They set off . . .
Which is correct?
Gerry's circular garden is 1200 m in diameter and has no fence. How far can a . . .
If Gerry gives Jane one apple, they will have the same number of apples. If . . .
At the end of each week, Gerry forgot 50% of what he knew the week before. At . . .
Guess!
What is the word coiled inside this circle?
I choose a 4-digit number in which the first digit is one-sixth the last, and . . .
Guess!
Which of the following is least like the others?
How many letters are there in the word that all smart students spell . . .
Three positive whole numbers have the same answer added together or when . . .
A grandmother prepared bowls of fruit for her family. The only fruits available . . .
If you make one word using each letter below only once, what place does the . . .
Three U.S. coins add up to $1. If one of them is not a half dollar, what is . . .
A five-digit number is evenly divisible by 9. If four of the five numbers are . . .
Using eight eights and addition only, make 1000. How many times did you use . . .
How long is a rope that is 8 meters shorter than another rope that is 5 times . . .
Gerry and Jane spent a week on an island and they ate only coconuts. Gerry . . .
Which goes next? N NE E SE S
What is the smallest integer that can be written with two digits?
In a room, there are 3 bosses, 2 wives, and a plumber who works for the . . .
Find the odd one out.
What triomino goes next?
Five teams of 4 students each met in a competition. Each student shakes the . . .
Crazy Logic. Choose a number.
If you were to spell out the numbers, how far would you have to go before . . .
Two American coins add up to 35 cents but one of them is not a dime. What is . . .
What is half of work and one third of gentleman?
If you take one third of GOOGLE and two thirds of ATT, what do you get?
A brick weighs 5 pounds and half a brick. What does a brick and a half weigh?
Zac's number is 5. Anna's number is 6. Bill’s number is 7. What is . . .
If today is the payday in Bob’s company, what happens in two days?
If One, Nine, and Eight gives ONE what is Two, Eight, and Nine ?
300 plus 150 and 300 minus X is the same thing. What is X?
What is missing?
The calculation is correct. Which number is hidden by the clouds?
When Pinocchio lies, his nose gets twice as long. When he tells the truth, his . . .
What letter goes next? A E F H I K L M N
In a room, there are 3 bosses, 2 wives, and a plumber. What is the least . . .
There are 2 matches. What is the least number of matches that can be added to . . .
There are two gods named Orbis and Fidelis, one on your left, the other on your . . .
There are 3 different positive integers that have the same answer whether . . .
THIS TEXT IS IN UPPER CASE. This text is in lower case. What is the . . .
On an European island, 18 are kids, 28 are divorced, 38 are married, and the . . .
Answer the traditional English-language nursery rhyme in the form of a riddle: . . .
Leslie Green asks: My neighbor Timmy has developed a complicated set of . . .
There are only two handshakes in a meeting: John shakes hands with a person, . . .
There are 4 playing cards face up in a line on a table. Each of the cards has a . . .
A 52-page newspaper "The Daily Dog News" consists of 13 double sheets. Edgar . . .
What is the main difference between the pictures on the left page and on the . . .
What is the main difference between the pictures on the left page and on the . . .
What is the main difference between the pictures on the left page and on the . . .
What is the main difference between the pictures on the left page and on the . . .
What is the main difference between the pictures on the left page and on the . . .
What is the main difference between the pictures on the left page and on the . . .
Gerry picks up several coins from the pirate chest. All but 5 have an eagle. . . .
What is the number that is equal to one half of one quarter of one tenth of . . .
Mensa question:
19 28 37 . . .
How many more numbers are . . .
The number of hours left today is half of the number of hours already passed. . . .
The total price of an apple and a tangerine is 39 cents. The total price of 2 . . .
A hockey team lost every fifth game and won 6 more than it lost. There are no . . .
The left clock runs slower at a rate of 6 minutes per hour. The second clock . . .
There are only four toys left in a shop. How many different purchases can be . . .
A food stand buys ice cream cones in packages of 8 and cartons of 14. What . . .
If three students eat three apples in 33 seconds, how long will it take nine . . .
A father wishes to divide a square piece of land among his five sons. He . . .
If 9 workers can build 9 houses in 9 months, then how many months would it . . .
A carnival game offers you the opportunity to bet $1 on a number from 1 through . . .
9 farmers grow 9 apples trees in 9 years. How many years would it take for . . .
You have eight dimes; seven are real and one is fake. All the real ones weigh . . .
A city hall floor is to be tiled in the following pattern. The hall measures . . .
It costs $24 to paint a cube, the cost being proportional to the surface area. . . .
The traveling salesman problem: a salesman has to visit 9 towns and return . . .
How many boxes measuring 1 x 2 x 3 can be packed into a container measuring 5 . . .
The diagram illustrates five villages, A, B, C, D, and E, with the distances . . .
Enclosed is a lamb using a 4-crosspiece log fence. What is the smallest . . .
How many different nonzero weights can you measure with a balance and three . . .
Apples are sold in bags of eleven that cost $11 per bag, or bags of nine that . . .
Three boys want to equally share three pancakes. The picture shows the . . .
Brad is framing a small flower box by four rectangular bricks. Each of the . . .
A jigsaw puzzle consists of 250 identically shaped pieces to spread on a plane. . . .
Find the best deal.
The Legend of Carthage: Queen Dido and her followers arrived in North Africa. . . .
You have 240 golden bricks identical in size and appearance but one is lighter . . .
I am selling my car. People come to my garage one at a time and make bids to . . .
I have a rectangular piece of cheese with a round hole. What line cuts the . . .
I place 1000 coins in two columns in a wooden box, and they fit nicely as . . .
The number of hours left today is a third of the number of hours already . . .
The total price of an apple and a tangerine is 39 cents. The total price of 2 . . .
A hockey team lost every fifth game and won 3 more than it lost. There are no . . .
The left clock runs slower at a rate of 5 minutes per hour. The second clock . . .
A food stand buys ice cream cones in packages of 28 and cartons of 12. What . . .
If three students eat three apples in 40 seconds, how long will it take six . . .
If 9 workers can build 9 houses in 9 months, then how many months would it . . .
You have 27 dimes; 26 are real and one is fake. All the real ones weigh the . . .
A city hall floor is to be tiled in the following pattern. The hall measures . . .
A city hall floor is to be tiled in the following pattern. The hall measures . . .
It costs $24 to paint a cube. Before painting, it was cut in four pieces by . . .
"Letter frequency. Accurate average letter frequencies can only be gleaned by . . .
I take half of the coconuts plus a coconut. What percentage of coconuts do I . . .
I want to construct a solid brick from wooden cubes. Its side ratio is 1 : 2 . . .
I place 11 chairs along the walls in an empty rectangular room. The number of . . .
The Lucas problem. François Édouard Anatole Lucas (1842-1891) was a French . . .
A red-line subway train arrives at a station every 5 minutes and stays for 30 . . .
Inspired by Morozkin's problem : Two children started at 6:00 and each . . .
A girl begins to ascend a mountain from its base at 8:00. She follows a . . .
Four people arrive at a river at night. There is a narrow bridge, but it can . . .
Every year, a man who had a million dollars at the beginning gives away half of . . .
Anna has 8 biscuits, Bill has 6, and Cindy has 1. They share them out equally. . . .
Job interview logic puzzle in a bank. Which of these pieces of information . . .
How many 1x1 squares fit into the large square with the side length 3.7? . . .
What is the minimum number of cuts needed to cut a log into 24 equal pieces? . . .
In a game, Anna and Bill take 1, 2, or 3 coins on each turn. The player to . . .
The size of a swimming pool is 25 x 12.5 meters. How many people must jump . . .
If John walks up an escalator at a rate of one step per second, 12 steps take . . .
Two proofreading programs, A and B, discovered 30 and 40 errors, respectively. . . .
Anna was planning to buy 10 souvenirs from the honesty shop. She wanted some . . .
Water is pumped into an empty swimming pool at a linearly increasing rate, . . .
A father has left 47 donkeys for you to distribute to his three sons; 1/2 . . .
Mary and John manage two different projects and they have a common budget. . . .
Management support accelerates the execution of a project by 10% during the . . .
There are 190 people in a company including the project managers and CEO. . . .
One by one, 40 cars enter a company parking lot with 40 assigned places. The . . .
You pay $6 to enter a game. You roll 2 dice. You then have two choices: you . . .
The State Tennis tournament starts with 128 players. How many rounds must be . . .
You have 3 coins. One is counterfeit and is either heavier or lighter than the . . .
A pirate boat is floating on a lake. The pirates throw a heavy chest with gold . . .
Seven trees are planted in a park, with exactly 3 meters between each . . .
What is the most money you can have in $1, $2, $5, $10, $20, and $50 bills and . . .
You have a large supply of 5kg and 12kg weights. Six 5kg weights and one 12kg . . .
I composed the numbers from strips of paper. Find the odd one out.
The water from an open swimming pool evaporates at a rate of 5 gallons per hour . . .
Jane and Gerry are lost in a forest. Gerry walks east, while Jane walks south . . .
I decided to use a password that includes 4 different numbers, with each number . . .
Gerry gave half of his money to Jane. Next day, she gave half of all her . . .
John is Jim's son. Jay is John's son. John is a doctor's son. His father . . .
Ten men met at a conference. It took 4 seconds for each man to shake hands . . .
A shopkeeper of a Dairy stands six feet tall and wears size 13 sneakers. What . . .
Kate was born on December 31st, yet her birthday always falls in the summer. . . .
Steve says that he will be X years old in year X
^{2}
. What will be . . .
What is missing?
A short word can be written forward, backward or upside down while remaining . . .
A boat has a ladder that has eight rungs. Each rung is 20cm apart. The bottom . . .
A worker prepared a block for a pyramid in a day. If every day the number of . . .
A girl walked along a level road and up a hill from home and back. Her pace . . .
There are 10 coins and 5 of them are fake. The real gold coins have the same . . .
If it rains at midnight in London, what are chances that it will be sunny in 72 . . .
The King of a far off land has just had the ballroom lights in his palace . . .
Before his death, a rich man signed his will. If my wife gives birth to . . .
A train departs from Lausanne to Zurich with 10 seconds delay and another one . . .
The ratio of women to men at a 100-employee company is 1 : 4. The company . . .
Make up one dollar by using 50 coins. What is the number of dimes that can be . . .
The boss of a 10 person company is always the last to arrive, and gets the . . .
Edgar chooses one of the double sheets of "The Daily Dog News". The two . . .
Lottery 6-digit numbers are from 000001 to 999999. A ticket is considered to . . .
There’s a tennis tournament with one hundred players. How many rounds does . . .