# Brain Teaser

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

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

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

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

Solve 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:

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

Solve 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

Solve 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

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

Solve 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

Solve 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

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

Solve 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

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

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

Solve 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

Solve 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

Solve 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

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

Solve 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

Solve 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√

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

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

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

Solve 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

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

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

Solve 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

Solve 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

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

Solve 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

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

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

Solve 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

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

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

Solve 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

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

Solve 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

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

Solve 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

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

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

Solve 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

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

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

Solve 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

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

Solve 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

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

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

Solve 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

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

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

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

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

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

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

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

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

Solve 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

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

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

Solve 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

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

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

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

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

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

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

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

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

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

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

Solve 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,

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

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

Solve 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

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

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

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

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

Solve 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

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

Solve 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

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

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

Solve 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.

Solve 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.

Solve 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

Solve 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

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

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

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

Solve 