Brain Teaser

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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