Puzzle Calendars

2023

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?