Brain Teaser

Question You have two empty containers — one that holds 9 liters and the other that holds 11.25 liters.   Using these moves

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Question You have two containers — one that measures 75 milliliters and one that measures 90 milliliters.   You can do any

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Question What is the minimum number of colors required to fill the regions of this graph so that no two adjacent (sharing the same

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Question What is the minimum number of colors required to fill the regions of this graph so that no two adjacent (sharing the same

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Question Every Londoner is either a human or a werewolf. Humans always tell the truth, while werewolves always lie.   Each of

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Question The two scales shown are balanced by non-zero weights. Which of the two scales (A or B) is balanced as well? Only A Only

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Question You make a pile of two books on a smooth wooden floor. Then, you push the bottom book along the floor, and both books acc

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Question A particular breed of dog can have black or yellow fur, and the fur’s texture can be straight or curly.   Two

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Question A function and its derivative are graphed as shown. Function A is in red and function B is in blue.   Which statemen

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Question An ant sitting in a ceiling corner of a cube-shaped room notices some honey in the opposite corner on the floor.   T

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Question According to the advertisement, the BrillCar can decelerate at a constant rate of 11.25 m/s2.   When it’s moving a

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Question The function graphed as shown is the derivative of one of these three functions. Which one?   A B C It isn’t possi

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Question A complete graph is a set of vertices with exactly one line segment connecting every pair of vertices.   To trace th

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Question Paco, Qi, Raj, Saba, and Tab read at least one book each month. Last month, they read as follows:   Qi read twice as

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Question You can change some of the addition signs to subtraction, multiplication, and division. Which result is impossible to obt

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Question To make the result equal zero, you need to change some of the addition signs to subtraction, multiplication, or division.

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Question Jade is using a pulley to lift a baby elephant to her room on the second floor (left image). If she improves her pulley a

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Question You can arrange the following instructions so that in the end the variables sum up to zero.   (Initially: X contains

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Question Sisters Molly and Nia are arguing whose turn it is to do the dishes. Molly suggests shuffling a deck of 20 cards numbered

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Question The mobile shown is balanced and all ornaments have positive weights. Which ornament is the heaviest?   A B C D

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Question Which method of connecting three identical bulbs will provide us with more light?   A B They’ll produce the sa

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Question Number Bunchers puzzles provide two or more boxes into which the numbers provided need to be sorted.   Herbie: “Th

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Question A queen bee wants to decorate her honeycomb so that adjacent (sharing the same border) hexagonal cells are different colo

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Question The fractal shown is made of a stack of shrinking concentric circles, starting from a yellow circle.   As the circle

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Question Ese and Oke are playing a game with two tennis balls — one yellow, one blue — concealed in a bag.   They let the

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Question Dark-grey gears have 10, yellow gears have 30, and light-grey gears have 60 teeth. We don’t know how many teeth the

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Question What weight on which side will balance the bottom scale shown?   1 kg on the left-hand side 1 kg on the right-hand s

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Question Which of the numbers below can’t you get by changing some of the + to -? 2 + 4 + 6 + 8 = 20   -8 0 6 8

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Question After a square is placed on the third scale, which side of the scale is heavier?   The left side The right side The

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Question In New Math City (NMC), streets follow a square grid with integer coordinates, and all distances are measured in terms of

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Question Which side of the last scale is heavier?   The left-hand side The right-hand side The scale is balanced We don’

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Question Rekha connected three identical bulbs and a battery as in the picture.   How can Rekha increase the total brightness

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Question Some railroad tracks are made of 20-meter-long metal rails bolted together by metal plates. The quintessential “cli

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Question In circle puzzles, dashed arrows indicate addition while solid arrows indicate multiplication. Which number will replace

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Question In the following two puzzles, you can change some of the addition signs to subtraction, multiplication, division, and con

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Question A fair die with 20 faces has each side labeled with a number from 1 through 10, with some labels appearing multiple times

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Question You’ve just met Maria and Nuria, sisters of your friend Daria. You can’t remember if either of them lives wit

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Question In the triangle shown, what is x?   30° 31° 32° 33°

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Question Shown are two squares of the same size. They’ve each been divided into many smaller squares. Which of the two large

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Question Which of these expressions is larger?   100! × 100! 99! × 101!

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Question What is the minimum number of matchsticks that must be removed from this arrangement to leave exactly two squares?  

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Question Which of these is the best fit to complete the pattern shown?  

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Question Andrei and Cristina would like to drink some tea, but they don’t want to wait too long for it to cool down. They bo

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Question A smartphone releases some energy as heat just as you do, but it has much less capacity to control its temperature: if a

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Question What is the least number of guards needed to completely guard this gallery of bovine art?   The guards cannot move,

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Question There are four people living in four differently colored houses, and every one of them has a different pet.   Annie

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Question In this puzzle, is Jasper a human or a werewolf? Each of these three Londoners is either a human or a werewolf. Humans al

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Question Nalani and Violet are treating themselves to ice cream at their favorite Jen & Berry’s. First, they choose one

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Question You play a casino game with these rules:   You roll a six-sided fair die. If you roll a non-6, you win the value of

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Question Sleepy the Cat was napping in a tree when he fell down. He landed on the ground — on all four feet, of course — with

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Question At any given point, the derivative of a function tells us its graph’s slope at that point. Given the function graph

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Question One of the three instructions below is a repetition of another. Given positive numbers A and B, you can rearrange all thr

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Question Daisy, Evie, Faye, Gwen, and Harry are comparing the numbers of students in their classes. These statements are all true:

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Question Geoff and Tetsu are playing a game in which they take turns removing cards from a deck of 16 cards. These are the rules:

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Question The top two scales shown are balances. How many circles will balance one triangle and one square? 3 4 5 6

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Question All of the ornaments hanging from this mobile have the same mass. Is the mobile balanced? Yes No It isn’t possible to d

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Question Two ants sit at the base of a cylindrical can with height 6 cm and circumference 16 cm. They want to get to the point at

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Question In this circle, a few angles are formed by two diameters and one additional radius. Which angle is larger, blue or yellow

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Question Two friends start playing a game with a token in the bottom-left corner of the grid. The game ends when the token reaches

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Question Pictured are a regular hexagon and the same hexagon stellated into a star. If the area of the hexagon is A, what is the a

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Question Dashed arrows mean to add. If each of the seven circles contains a unique non-negative integer, how many values can the m

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Question The lower base of this trapezoid is three times as long as its upper base. The area of the yellow triangle equals 45. Wha

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Question In the pictured triangles, the angle measures are as follows:   ∠BAC=y−12° ∠ADB=x+64° ∠ABD=y+10° ∠BDC=x

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Question The product of Ivy’s, Joshua’s, Kylie’s, and Logan’s ages is 1296.   Which of these numbers

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Question Leticia is writing a test question for her math students. She wants them to find solutions to the equation x+y+z=12, wher

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Question On a school trip, Otto tries to take a selfie with the bottom of a deep well in the background, but the phone slips out o

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Question We can arrange the following instructions in six different ways: set X to X plus Y set Y to X minus Y set Z to X times Y

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Question Nikesh wants to know how much the three textbooks required for the brilliantology course will cost him. By mistake, he re

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Question A rectangular box of chocolates sits on the ground. Its base is a square of side length 4 inches, while its height is 6 i

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Question The figure shown is composed of a triangle and a trapezoid and has perimeter 18. What is its total area? 21√3 / 4 23√

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Question Out of 404 students of Brilliant Language School, 192 learn German, 162 Spanish, and 122 French. Every student learns at

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Question We want to trace the entire figure shown, using these rules: You can start at any intersection on the figure You cannot l

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Question Dorian wants to build a rectangular-shaped house on a plot of circular land with radius 6. What is the largest possible a

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Question Anika is training for a running competition. At first, she jogs with a constant speed of 4 m/s. Then, for the last 60 m o

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Question You’re given four boxes, each containing three gold/silver coins as shown. You pick one box at random and remove on

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Question What is the largest number of statements below that can be simultaneously true? All the statements below this one are fal

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Question 512 small cubes are arranged into a larger 8×8 cube, and then the outside of the larger cube is painted. Some of the sma

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Question Bjorn holds two water balloons on a platform from 20 m high. As he throws one of the balloons straight down, the other on

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Question After a tennis match, the four players got their gear mixed up. Each player accidentally took the racket of one player an

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Question From which point should we support the pictured mobile to make it hang balanced? A B C D It isn’t possible to balan

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Question You have two large containers — one that holds 40 liters and the other that holds 56 liters.   You’ve been t

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Question How many four-digit numbers can we create by rearranging digits of 2021? All four of the digits must be used exactly once

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Question You drop a stack of three balls. The bottom ball is the heaviest, with the middle ball much lighter and the top ball much

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Question Jaz makes circular necklaces by stringing black and gold beads together. She wants to count how many different necklaces

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Question At a university, the portraits of its 50 presidents line a hallway of the student center. Every year, 50 students pull th

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Question Your goal is to measure out 7 liters of water. You have one empty 12-liter container, and you may choose one other contai

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Question There are x regular polygons, all with n sides of length 1 arranged in a row as the triangles, squares, and pentagons are

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Question In a grassy field, a goat is tethered by a rope with length 6 to the corner of a rectangular shed with side lengths 4 and

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Question Look at the program above:   Imagine running this program 21 times, with each of the integers from -10 to 10 as the

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Question Only one-digit numbers can start with a zero. If every letter corresponds to a different digit, what is A+B+C+D? 5 9 19 2

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Question The mobile shown is balanced. Karen is quite happy with her perfectly balanced mobile.   Karen’s friend Juli i

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Question The yellow pentagon is inside of a rectangle. What is the yellow-shaded area? 52 68 72 74 80

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Question The outer figure is a square and the line from each vertex bisects its opposite side. What is the area of the central whi

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Question Alma, Baptiste, and Cadence equally share eighteen identical springs, and each person designs their own spring system for

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Question If the three elephants have equal weights, which elephant (or elephants) falls downward? Assume the pulley and rope weigh

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Question There is a three-digit code where only the digits 1 through 5 are possible. Each of the numbers shown has exactly one dig

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Question Wisely You have two empty containers: one that holds 6 liters and the other that holds 7.5 liters. completely fill a cont

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Question The factorial of n (written n!) is the product of every positive integer up to n. For example, 4! = 1 x 2 x 3 x 4 = 24. L

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Question The four puzzles pieces shown fit into the 4 x 4 grid without reflection or rotation. Based on these clues: No letter is

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Question In the triangles formed by intersecting lines, the gray angles are equal. Both the blue and yellow figures are squares. W

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Question dogs have a mean weight of 50 pounds. If two of the dogs’ weights are 220 pounds and 80 pounds, what is the largest

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Question You have one container that holds 8 liters and another that holds 12 liters. You can do any of the following: Completely

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Question Angles of the same color are identical. What is the measure of the blue angle? 10° 20° 30° 40° 50°

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Question A lune is an area formed by two circles. When two circles intersect, two lunes are formed: the non-intersecting portions

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Question What is the minimum number of colors required to fill the regions of this graph so that no two adjacent (sharing the same

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Question Angles of the same color have the same measure. What is the measure of the green angle? 2 4 5 6 8

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Question You have one container that holds 9 liters and another that holds 12 liters. The smaller container already has 4 liters o

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Question A three-legged creature has an unorganized sock drawer with 4 red socks, 6 blue socks, and 8 yellow socks. The creature r

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Question Three rectangles have areas of 72, 80, and 130. We arrange them so they overlap, as shown. What is the total shaded area?

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Question Using the rules below, you’d like to be able to trace the figure. You can start at any intersection point on the fi

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Question Lin, Malik, Nia, Ophelia, and Pradeep live on different streets in the same neighborhood.   The following informatio

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Question All circles in the dartboard have the same center. Each circle has half the radius of the previous circle. The colors alt

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Question Two squares with side lengths 4 and 6 are arranged side by side. Which value is the closest to the area of the yellow reg

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Question Edgar and Beatrix are playing the “100” game, with the following rules: What is the measure of the green angl

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Question You have one container that holds 15 liters and another that holds 9 liters. The larger container already has 11 liters o

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Question Areas Each number inside a colored region is the area of that region. What is the value of x? 17 18 19 20

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Question The four puzzle pieces in the image fit into the 4×4 grid without rotation or reflection. Based on these clues, find

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Question The fuel used to propel spaceships can’t depend on atmospheric oxygen as a reactant, since they might not be operat

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Question Your twin leaves you on Earth and flies away at 0.8c0.8c0.8c, then turns around nearly instantaneously and returns at the

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Question Angles of the same color have the same measure. What is the measure of the green angle? 30° 35° 40° 45°

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Question A young mouse is weighing an important decision.   The sound of human footsteps is approaching, and the mouse needs

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Question How many squares in this grid contain the orange square? 14, 18, 19, 55  

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Question Each letter stands for a distinct digit, and if letters are different, so are the digits they represent. What digit is E?

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Two trains, each traveling at a speed of are headed toward each other on the same track. At the exact moment the trains are apart,

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Art gallery problems involve finding an unmoving guard (or guards) who can “see” the entire gallery. A guard is able t

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Can Area Reveal Volume? Consider the two shapes inside the two identical cylinders whose radius is equal to its height.

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Can a 10 x 10 grid of cells be covered by 25 1 x 4 pieces?

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All four Kings from a deck of cars are placed face down on a table in a random order. You select two of them, and if both are the

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A system of two symmetrical, identical, water-filled jars is fixed on a turntable. Each jar has a cork—attached to the bottom by

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Question Two of the following statements are true and the other one is false: This statement is true. The first statement is false

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True or False? The sum of two consective triangular numbers is always a square numbers!

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Which string will break first? a. Horizontal String!, b. Vertical String!, c. Both will break at the same time

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If a number n can be factored as a×b then n will appear in row a+b-1. For example the number 6 appears in row 1+6-1=6 but also ro

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Nine consecutive integers are placed in the squares of a 3x3 grid. Every column, every row, and every diagonal add up to the same

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What time is it?

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All four Kings from a deck of cards are placed face down on a table in a random order. You select two of them, and if both are the

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How many quadrilaterals are drawn in this figure? Hint: Be sure to count both convex and concave quadrilaterals.

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A light ray emitted from a vertex of this isosceles triangle reflects 6 times before reaching another vertex. What is the total

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Place the ten integers 2 through 11 into the ten squares such that the sum of the numbers in each 2x2 square is the same value, P.

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Regular hexagon patio blocks of area 1 are used to outline the garden shown, with n=5 blocks on each side placed edge to edge.

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An ant named Honey is kept outside a solid cube on a leash, which extends to twice the side length of the cube. The leash can b

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What's the minimum number of straight cuts required to cut a circle into 7 regions of equal area? There are a number of ways t

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The area of the whole rectangle is 160 and the area in red is 12. What is the area in green?

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Seven identical regular hexagons are arranged in a honeycomb pattern. If each hexagon has area 8, what is the area of the red tria

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Magnus, Garry, and Fabiano are playing in a badminton event. In this event, after two players face off for a set, the winner stays

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