Olympiad Numbers and Arithmetic
Find the smallest positive integer that must be . . .
Olympiad Numbers and Arithmetic
Which gives the smallest answer?
Olympiad Numbers and Arithmetic
The first person is 100 cm tall. Each subsequent . . .
Olympiad Numbers and Arithmetic
Find the hundreds digit (third digit from the . . .
Olympiad Numbers and Arithmetic
Which gives the largest answer?
Olympiad Numbers and Arithmetic
How many 2-digit integers are there in which the . . .
Olympiad Numbers and Arithmetic
How many digits are in the product of 2101 and 599?
Olympiad Numbers and Arithmetic
Choose the answer without using a calculator. . . .
Olympiad Numbers and Arithmetic
How many sets of at least two consecutive . . .
Olympiad Numbers and Arithmetic
On this target, I scored exactly 80. How many . . .
Olympiad Numbers and Arithmetic
In how many ways can you choose 4 of the first 8 . . .
Olympiad Numbers and Arithmetic
Which is the sum of all digits of the decimal . . .
Olympiad Numbers and Arithmetic
The sum of digits of a two digit number X is Y. . . .
Olympiad Algebra
Find the sum of all the elements of this finite . . .
Olympiad Algebra
The last digit of the number 333 is:
Olympiad Algebra
A perfect cube is an integer whose cube root is . . .
Olympiad Algebra
Eugenia used 192 digits to number the pages in . . .
Olympiad Algebra
How many digits are in the result of the . . .
Olympiad Algebra
How many 2-digit numbers have a tens digit that . . .
Olympiad Algebra
Which of the following gives the biggest answer?
Olympiad Algebra
What is the smallest integer that is 4 times the . . .
Olympiad Algebra
Choose the answer without using a calculator. . . .
Olympiad Algebra
Find the last digits of the product. (7 x 5 x . . .
Olympiad Algebra
A square game board begins with a dark square . . .
Olympiad Algebra
What is the largest product of positive integers . . .
Olympiad Algebra
F = (x-a)(x-b)(x-c) . . . (x-x)(x-y)(x-z) Find . . .
Olympiad Geometry
How many of the letters in the Russian alphabet . . .
Olympiad Geometry
The letter 'A' is symmetrical. A symmetrical . . .
Olympiad Geometry
For which letter did I use the smallest amount of . . .
Olympiad Geometry
Each square is 1 square unit. What is the area . . .
Olympiad Geometry
Which shape has the largest shaded region in . . .
Olympiad Geometry
The figure shows a regular hexagon. What is . . .
Olympiad Geometry
I strike a pool ball from corner A of the . . .
Olympiad Geometry
The squares have side lengths of 2 and 4. Find . . .
Olympiad Geometry
The figure shows a regular octagon. What is . . .
Olympiad Geometry
The diagram illustrates a row of three squares . . .
Olympiad Geometry
The picture shows two identical squares with . . .
Olympiad Geometry
Two lines and two diagonals are drawn through the . . .
Olympiad Geometry
How many equilateral triangles can you create . . .
Olympiad Geometry
A boy cuts a cardboard circle and only cuts 5 . . .
Olympiad Geometry
How many planes of symmetry does a cube have?
Olympiad Geometry
How many boxes measuring 0.1m x 0.1m x 6.9m can . . .
Olympiad Geometry
A boy stacked colored cubes in a square pyramid . . .
Olympiad Geometry
A six-pointed regular star consists of two areas. . . .
Olympiad Geometry
The figure shows a red equilateral triangle . . .
Olympiad Geometry
There are 2 identical circles. Circle A remains . . .
Olympiad Geometry
How many squares can you make using twelve . . .
Olympiad Geometry
Divide the analog watch face with two straight . . .
Olympiad Geometry
Twenty matchsticks form five squares (one 3x3 and . . .
Olympiad Geometry
Which of the nets can be folded into a box with a . . .
Olympiad Geometry
The blocks of ice are of the same height. . . .
Olympiad Geometry
A ladder leans against a vertical wall. The top . . .
Olympiad Geometry
All inner lines connect the corners of the big . . .
Olympiad Geometry
Among the following shapes of equal area, which . . .
Olympiad Geometry
The sizes of the sealed bottle with water are . . .
Olympiad Geometry
How many equilateral triangles can you make using . . .
Olympiad Geometry
In a 3 x 3 grid, there are 8 lines that contain . . .
Olympiad Geometry
How many triangles are there?
Olympiad Geometry
The following pattern is cut and folded to a . . .
Olympiad Geometry
I fold a square piece of paper in half four times . . .
Olympiad Geometry
Every face of a cube has at least one white . . .
Olympiad Geometry
How many squares can be formed by joining four of . . .
Olympiad Geometry
How many more lines can I draw to make a shape . . .
Olympiad Geometry
Which of these parts has the smallest area?
Olympiad Geometry
What is the maximum number of possible points of . . .
Olympiad Geometry
The diameter of one hair is 0.02 mm. Estimate . . .
Olympiad Geometry
I want to place together five identical shapes . . .
Olympiad Geometry
Compare areas F and G
Olympiad Geometry
The left picture shows nine dots arranged in a 3 . . .
Olympiad Geometry
What is the sum of the marked angles?
Olympiad Geometry
The picture shows six equilateral triangles. The . . .
Olympiad Geometry
The shaded rhombus is formed by joining vertices . . .
Olympiad Geometry
Which of these diagrams could be drawn without . . .
Olympiad Geometry
The diagram shows 15 billiard balls that fit . . .
Olympiad Geometry
Fifteen billiard balls perfectly fit into a . . .
Olympiad Geometry
What is the smallest number of segments that . . .
Olympiad Geometry
Which of these diagrams could be drawn completely . . .
Olympiad Geometry
The picture shows the areas of three rectangles. . . .
Olympiad Geometry
This shape was formed by removing a small cube . . .
Olympiad Geometry
I want to cut round bread into eight equal . . .
Olympiad Geometry
A girl wants to cut the paper into several equal . . .
Olympiad Geometry
How many colored four-unit shapes can be placed . . .
Olympiad Geometry
Two triangles form seven separate regions. What . . .
Olympiad Geometry
What fraction of the large equilateral triangle . . .
Olympiad Geometry
Four matchsticks form a square. How many . . .
Olympiad Geometry
There are six ways to travel from point S to . . .
Olympiad Geometry
The game Battleship (Battleships or Sea Battle) . . .
Olympiad Geometry
Seven squares with side length of 1, 2, 2, 2, 3, . . .
Olympiad Geometry
I want to cut this shape into four pieces all of . . .
Olympiad Geometry
How many circles are needed to separate each star . . .
Olympiad Geometry
I would like to cut the shape into the fewest . . .
Olympiad Geometry
The colored figure at the picture consists of . . .
Olympiad Geometry
A, B, and C are squares with sides of length 1; . . .
Olympiad Geometry
What is the maximum number of pieces that an . . .
Olympiad Geometry
I arrange 10 points so that 3 lines each go . . .
Olympiad Geometry
Find the radius of the circle.
Olympiad Data Analysis
How many stars will be in the fourth line of the . . .
Olympiad Data Analysis
Bob is rolling two dice and adding the numbers on . . .
Olympiad Data Analysis
The average of eleven numbers is 9 and the . . .
Olympiad Data Analysis
Fifteen numbers have an average of 15. Five of . . .
Olympiad Data Analysis
Three boxes contain two coins each. One . . .
Olympiad Data Analysis
If two dice are rolled 72 times, how many times . . .
Olympiad Data Analysis
I roll two dice. What is the probability that . . .
Olympiad Data Analysis
Five students put their sandwiches into five . . .
Olympiad Data Analysis
Four kinds of apples are combined in a box. I . . .
Olympiad Data Analysis
By drawing two marks on a wooden ruler, we can . . .
Olympiad Data Analysis
John is sick 6 days per year. The probability of . . .
Olympiad Data Analysis
A boy begins walking from his starting point. . . .
Olympiad Data Analysis
What is the units digit of 1! + 2! + 3! + ... + . . .
Olympiad Data Analysis
Two princes and two princesses are ready to . . .
Olympiad Data Analysis
A password includes only two different digits. . . .
Olympiad Data Analysis
Four cowboys have a meeting in a saloon. Each . . .
Olympiad Data Analysis
Two dice are thrown. All the numbers on the ten . . .
Olympiad Data Analysis
After a gun fired in a saloon, 75% of the cowboys . . .
Olympiad Data Analysis
If we set out by ranks of 10, we will be one . . .
Olympiad Data Analysis
Which shape can not be folded to form an open box?
Olympiad Data Analysis
Two dice are thrown. Two numbers are . . .
Olympiad Data Analysis
Two cards are randomly chosen. Two numbers are . . .
Olympiad Data Analysis
What is the average of the smaller of three . . .
Olympiad Data Analysis
Russian roulette problem: Two cowboys use a . . .
Olympiad Data Analysis
Each of four children chose one of these cards. . . .
Olympiad Data Analysis
Bob the plumber has 10 pockets and 60 nuts. He . . .
Olympiad Data Analysis
Forty numbers are written in a row. The average . . .
Olympiad Logic
Each of four children has a photo. Anna and . . .
Olympiad Logic
How many letters are there in the correct answer . . .
Olympiad Logic
There are 20 students in a class. 12 students . . .
Olympiad Logic
Tom writes a total of forty words on five blank . . .
Olympiad Logic
Brad has as many brothers as sisters. How many . . .
Olympiad Logic
The total weight of Bob and his sister Anna is . . .
Olympiad Logic
If you write all numbers from 0 to 109, which . . .
Olympiad Logic
Ten men met at a conference. Each man shook . . .
Olympiad Logic
The product of three consecutive whole numbers is . . .
Olympiad Logic
Three referees, A, B, and C, are at the corners . . .
Olympiad Logic
Eugenia, the magician, receives a 50% discount . . .
Olympiad Logic
Four friends tried to guess the number of sheep . . .
Olympiad Logic
How many cubes will balance one sphere?
Olympiad Logic
Alex needs six tacks to fix two rectangular . . .
Olympiad Logic
The picture shows the first five notes of the . . .
Olympiad Logic
There is a set of 10 numbers. Five numbers are . . .
Olympiad Logic
John's dad pays him 80 cents for each correct . . .
Olympiad Logic
Five students put their sandwiches into five . . .
Olympiad Logic
Eugenia's grandmother bought a new car for . . .
Olympiad Logic
I want to fill a 4-litre bucket with milk using a . . .
Olympiad Logic
In the first week John made $1. He made 5 times . . .
Olympiad Logic
Anna's income is seven-eighths that of Beatrice. . . .
Olympiad Logic
Anna wants to score exactly 33 points. The ducks . . .
Olympiad Logic
The diagram shows some of the results of a . . .
Olympiad Logic
How many times do the clock hands form a . . .
Olympiad Logic
John read a 165-page book in 11 days. Every day, . . .
Olympiad Logic
The first six numbers in a sequence are shown on . . .
Olympiad Logic
The number 99! is very big. How many zeros are . . .
Olympiad Logic
What is the sum of 99 consecutive integers, if a . . .
Olympiad Logic
I arrange five marbles randomly in a ring. . . .
Olympiad Logic
A girl was born in 20th century. Take away from . . .
Olympiad Logic
Mr. Smith can read 1 page in 2 minutes. His wife . . .
Olympiad Logic
The twins are of the same height. They place . . .
Olympiad Logic
How many two-digit integers are there in which . . .
Olympiad Logic
Ten years ago, Bob was three times as old as . . .
Olympiad Logic
Statement 1: There are 3 animals in a room. . . .
Olympiad Logic
How many straight lines are needed to separate . . .
Olympiad Logic
Two gears, one with 11 teeth and the other one . . .
Olympiad Logic
1. At least 1 of these 6 statements is false 2. . . .
Olympiad Logic
You take half of syrup and mix it with the water, . . .
Olympiad Logic
The matchsticks make a spiral that goes . . .
Olympiad Logic
The figure shows a triangle made of discs. I . . .
Olympiad Logic
Two rectangles enclose five regions. Find 2 . . .
Olympiad Logic
In-Out Machine transforms 111121 into 100. The . . .
Olympiad Logic
An analogue clock loses 15 minutes each hour. . . .
Olympiad Logic
What is the largest number you can write with . . .
Olympiad Logic
Sixteen European teams enter a football . . .
Olympiad Logic
A password consists of five digits, 0-9. How . . .
Olympiad Logic
The product of 2 integers is 1000. Find the . . .
Olympiad Logic
What is the condition for the smallest ten-digit . . .
Olympiad Logic
A lady, attempting to avoid revealing her real . . .
Olympiad Logic
A dozen balls cost you $40. You get every fifth . . .
Olympiad Logic
The pages of a book are consecutively numbered . . .
Olympiad Logic
The addition shown here has 21 terms and the last . . .
Olympiad Logic
There is a total of 6 squares whose vertices are . . .
Olympiad Logic
I put $990 into 10 envelopes. I try to compose . . .
Olympiad Logic
Alex has bills of different dollar values. There . . .
Olympiad Logic
On January 1st, Anna and Bill have $100 each. . . .
Olympiad Logic
Four painters can complete a painting job in 20 . . .
Olympiad Logic
An integer consists of 2010 digits such that any . . .
Olympiad Logic
Twelve couples met at a party. Each person shook . . .
Olympiad Logic
The time on a digital clock reads 9:43. What . . .
Olympiad Logic
There are a number of apples, all of different . . .
Olympiad Logic
There are four brothers in a family. The sums of . . .
Olympiad Logic
In how many ways can the name ALEX be spelt out, . . .
Olympiad Logic
What number should replace the question mark?
Olympiad Logic
What number should replace the question mark?
Olympiad Logic
Find the missing figure.
Olympiad Logic
Which shape fits in the missing space to complete . . .
Olympiad Logic
Three children and two adults want to cross a . . .
Olympiad Logic
Which of these diagrams could be drawn without . . .
Olympiad Logic
I wrote all the numbers from 0 to 999. Which . . .
Olympiad Logic
How many different ways are there to go from A to . . .
Olympiad Logic
Each of these seven cells contains one number . . .
Olympiad Logic
Two apples and two peppers have the same weight . . .
Olympiad Logic
There are eight buckets; four of them are filled . . .
Olympiad Logic
I enclosed 9 apple trees using a large square . . .
Olympiad Logic
A group of gentlemen visited a produce shop. . . .
Olympiad Logic
A number is said to be perfect if it is equal to . . .
Olympiad Logic
The matchsticks make four small squares and one . . .
Olympiad Logic
Multiply all positive two-digit numbers. How . . .
Olympiad Logic
Which pair of two shapes is not like the others?
Olympiad Logic
A banker forgets which key fits in which of three . . .
Olympiad Logic
You have four piles: three piles with real coins . . .
Olympiad Logic
How many times do the two hands of a clock point . . .
Olympiad Logic
How many zeros are there at the end of . . .
Olympiad Logic
Use each digit, 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, . . .
Olympiad Logic
Logic puzzle. There are three mothers and three . . .
Olympiad Logic
Tricky Equation Puzzle: the equation below is . . .
Olympiad Logic
Anna ran in the north direction at a speed of 8 . . .
Olympiad Logic
I must balance any whole number load from 1 kg to . . .
Olympiad Logic
How many different lines can you draw through . . .
Olympiad Logic
A kitten has a 50/50 chance to be male or female. . . .
Olympiad Logic
If each row and each column of the square must . . .
Olympiad Logic
2889 digits are used to number the pages of a . . .
Olympiad Logic
Find the next letter in the sequence.
Olympiad Logic
A bee crawls along the sides of the honeycomb . . .
Olympiad Logic
Twenty-two performers have numbers 1 to 22. A . . .
Olympiad Logic
How many three-digit numbers containing only even . . .
Olympiad Logic
What is the largest digit in the product of . . .
Olympiad Logic
I would like to plant ten trees in five rows of X . . .
Olympiad Logic
A farmer puts several pigs into three pens. . . .
Olympiad Logic
How old is the youngest sister if the product of . . .
Olympiad Applied Math
The number of hours left today is half of the . . .
Olympiad Applied Math
The total price of an apple and a tangerine is 39 . . .
Olympiad Applied Math
A hockey team lost every fifth game and won 6 . . .
Olympiad Applied Math
The left clock runs slower at a rate of 6 minutes . . .
Olympiad Applied Math
There are only four toys left in a shop. How . . .
Olympiad Applied Math
A food stand buys ice cream cones in packages of . . .
Olympiad Applied Math
If three students eat three apples in 33 seconds, . . .
Olympiad Applied Math
A father wishes to divide a square piece of land . . .
Olympiad Applied Math
If 9 workers can build 9 houses in 9 months, . . .
Olympiad Applied Math
A carnival game offers you the opportunity to bet . . .
Olympiad Applied Math
9 farmers grow 9 apples trees in 9 years. How . . .
Olympiad Applied Math
You have eight dimes; seven are real and one is . . .
Olympiad Applied Math
A city hall floor is to be tiled in the following . . .
Olympiad Applied Math
It costs $24 to paint a cube. Before painting, . . .
Olympiad Applied Math
How many green tiles are there?
Olympiad Applied Math
The traveling salesman problem: a salesman has to . . .
Olympiad Applied Math
How many boxes measuring
1 x 2 x 3 can be packed . . .
Olympiad Applied Math
The diagram illustrates five villages, A, B, C, . . .
Olympiad Applied Math
Enclosed is a lamb using a 4-crosspiece log . . .
Olympiad Applied Math
How many different nonzero weights can you . . .
Olympiad Applied Math
Apples are sold in bags of eleven that cost $11 . . .
Olympiad Applied Math
Four boys want to equally share three pancakes. . . .
Olympiad Applied Math
Brad is framing a small flower box by four . . .
Olympiad Applied Math
A jigsaw puzzle consists of 250 identical pieces . . .
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