What’s the ratio of the areas of the triangle and the crescent-shaped “lune” formed by two circular arcs?
How many non-attacking knights can be placed on a chessboard?
A deck of 52 cards is shuffled. On average, how many cards do you expect to remain in exactly the same position as before the shuffle?
What is the area of the shape enclosed by these six hat mono-tiles?
What’s the next number in this sequence? 1, 3, 4, 7, 11, 18, ?, ?
How many squares does the diagonal of a 15 × 27 rectangle pass through?
Here is a 3 × 4 grid of stamps. How many different ways are there to tear off four stamps (still joined together along their sides)?
What proportion of this bottle is filled with water?
Can you cut this right-angled triangle with smaller sides 1 and 2 into five identical triangles, each similar to the big triangle?
How many numbers between 1 and 9999 consist of at most two different digits?
How many of these 15 coins arranged in a triangle do you have to move, so that the triangle points downwards?
One cut divides a cake into 2 pieces. Two cuts can divide it into 4 pieces. Three cuts can divide it into 7 pieces. What is the maximum number of pieces you can make with 10 cuts?
Five people A, B, C, D and E are seated randomly around a round table. What is the probability that A and B are next to each other?
How many squares can you make using four of these points as vertices?
Rearrange these 8 prime numbers and 1 into a magic square where every row and column adds up to the same number.
A semicircle is placed inside a square of size 1. What is the diameter d of the semicircle?
You and your friend both throw a fair die. What is the probability that you get a higher number?
How many different necklaces can be made using five identical blue beads, and two identical yellow beads?
Use a single, straight-line to cut this shape into two pieces that can be rearranged into a square.
What is the sum of all the digits of the numbers from 1 to 100? 1 + 2 + 3 + … + (9 + 9) + (1 + 0 + 0)
Can you make all these shapes using the seven Tangram pieces?
What’s the probability that the ball will land in bucket B?
All three circles have radius 1. What is the radius of the larger semicircle?
What is the least number of moves needed to transfer all seven disks from the first tower to the last, without placing a larger disk on a smaller one?
2022
Can you cut each of these two shapes into four identical pieces?
What six digits should be placed on the second die, so that the distribution of the sum of both dice is the same as two normal dice? The first die contains faces numbered 1, 2, 2, 3, 3, 4.
Place the digits from 1 to 7 into each of these regions, so that every circle has the same sum.
What is the area of the semicircle, which is placed symmetrically inside a quarter circle?
Alice said Bob did it. Bob said Alice did it. Carol said Alice didn’t do it. Dan said it was either Alice or Carol. Only one person is telling the truth. Who did it?
Can you express 7/8 as a sum of distinct “unit fractions” of the form 1/x?
How many different ways are there to connect four cubes? Every cube needs to touch at least one other cube, and faces need to line up. You can ignore rotations or reflections.
Can you use eight 8s, together with mathematical symbols like + and –, to make 1000?
What is the ratio of the perimeters of the circumscribed and inscribed hexagon of a circle?
Two athletes are running at constant speeds on a circular track. If they head in opposite directions, they meet after one minute. If they head in the same direction, they meet after one hour. What is the ratio of their speeds?
You have two jugs with volumes 3 and 5 liters, but no markings. Can you use them to get exactly 4 liters of water?
What’s the next number in this sequence? 441, 961, 691, 522, 652, 982, 423, …
A shop sells chocolates in boxes of 6, 9 or 20. What is the largest amount of chocolates that is impossible to buy? For example, it is impossible to buy 10 chocolates using boxes of 6, 9 or 20.
A circle is bounded by two quarter circles in a square. What is its area?
If 5 balls are placed at random into 5 buckets, what is the probability that exactly one bucket remains empty?
How many times per day do the minute and hour hands on a clock form a straight line?
What is the area of the intersection of these two rectangles of size 1 × 2?
What is the sum of the first six cube numbers? What about the first 10 cube numbers?
Can you find a 10-digit number, so that: the first digit is the number of zeros in that number, second digit is the number of 1s, … tenth digit is the number of 9s?
Three squares are placed next to each other. What is the sum of the three angles a, b and c?
How many triangles are in this diagram?
You randomly draw two cards from a standard deck of 52 cards. What is the probability that both cards have either the same suit or the same number/symbol?
What is the fewest number of weights you need, to be able to balance any weight from 1 to 40 on a 2-sided scale?
What is the size of the 10th square in this sequence? What is the total area after 10 iterations?
