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

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

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

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

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

SolveQuestion 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

SolveQuestion 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

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

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

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

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

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

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

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

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

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

SolveQuestion 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

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

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

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

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

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

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

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

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

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

SolveQuestion 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

SolveQuestion 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

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

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

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

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

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

SolveQuestion 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

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

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

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

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

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

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

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

SolveQuestion 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

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

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

SolveQuestion 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

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

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

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

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

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

SolveQuestion 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

SolveQuestion 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

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

SolveQuestion 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

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

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

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

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

SolveQuestion 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

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

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

SolveQuestion 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

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

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

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

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

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

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

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

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

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

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

SolveQuestion 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

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

SolveQuestion 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

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

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

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

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

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

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

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

SolveQuestion 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

SolveQuestion 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

SolveAll 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

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

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

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

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

SolveIf 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

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

SolveWhat time is it?

SolveAll 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

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

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

SolvePlace 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.

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

SolveAn 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

SolveWhat'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

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

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

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

Solve