Did you solve it? The deductive decade – ten years of Monday puzzzles

The Guardian

09-06-2025

To celebrate ten years of this column, this morning I selected ten puzzles from the Monday Puzzle archives. Here they are again with solutions. Click on the solutions to be taken to the original columns, which have full explanations.
1. Bat and ball
Three friends (A, B and C) are playing ping pong. They play the usual way: the winner stays on, and the loser waits their turn again. At the end of the day, they summarise the number of games that each of them played:
A played 10
B played 15
C played 17.
Who lost the second game?
Solution A
2. Tricky trams
Why are the tram's overhead cables positioned to make a zigzag, rather than straight line?
Solution The metal structure on the roof of the tram, the pantograph, rubs against the cable as the tram moves forward. If the cable was in a straight line, it would rub the same point on the pantograph, which would begin to fray. But if the cable is in a zigzag, the rubbing happens evenly across the top of the pantograph, and the pantograph wears down less quickly.
3. Read the question
3. What is never odd or even?
Solution 'never odd or even' is a palindrome, i.e. it reads the same back to front.
4. Catch the cat
A straight corridor has 7 doors along one side. Behind one of the doors sits a cat. Your mission is to find the cat by opening the correct door. Each day you can open only one door. If the cat is there, you win. If the cat is not there, the door closes, and you must wait until the next day before you can open a door again.
If the cat was always to sit behind the same door, you would be able to find it in at most seven days, by opening each door in turn. But this mischievous moggy is restless. Every night it moves randomly either one door to the left or one to the right. Although if it is behind the first or last door, it has only one option for where it can move.
How many days do you now need to make sure you can catch the cat?
Solution ten days
5. Mystery number
I have a ten digit number, abcdefghij. Each of the digits is different, and
a is divisible by 1
ab is divisible by 2
abc is divisible by 3
abcd is divisible by 4
abcde is divisible by 5
abcdef is divisible by 6
abcdefg is divisible by 7
abcdefgh is divisible by 8
abcdefghi is divisible by 9
abcdefghij is divisible by 10
What's my number?
[To clarify: a, b, c, d, e, f, g, h, i, and j are all single digits. Each digit from 0 to 9 is represented by exactly one letter. The number abcdefghij is a ten-digit number whose first digit is a, second digit is b, and so on. It does not mean that you multiply a x b x c x…]
Solution 3816547290
6. Disappearing cub
This picture has not been doctored. Explain why the reflection has a yellow lion cub.
Solution: The cub is camouflaged by a cleverly-coloured flap
7. Crazy triangle
Show that there is a triangle, the sum of whose three heights is less than 1mm, that has an area greater than the surface of the Earth (510m km2).
Solution
Here's one:
8. Deck dilemma
Your friend chooses at random a card from a standard deck of 52 cards, and keeps this card concealed. You have to guess which of the 52 cards it is.
Before your guess, you can ask your friend one of the following three questions:
is the card red?
is the card a face card? (Jack, Queen or King)
is the card the ace of spades?
Your friend will answer truthfully. What question would you ask that gives you the best chance of guessing the correct card?
Solution It doesn't matter. In all three cases, your chance of guessing the correct card is 1 in 26.
9. The question with no question
(a) All of the following.
(b) None of the following.
(c) Some of the following.
(d) All of the above.
(e) None of the above.
[Just to reassure you, nothing has been omitted here.]
Solution (b)
10. Triangle fold
Find a way to fold a square piece of paper into an equilateral triangle. The triangle can be of any size.
Solution Here is one way, that uses the side length of the square as the side length of the triangle.
I hope you enjoyed these puzzles. I'll be back in two weeks.
Sources: 1. Adrian Paenza, 2. Kvantik magaizine, 3. Des MacHale, 4. New York Times. 5. John Conway, 6. Matt Pritchard, 7. Trần Phương, 8. Henk Tijms, 9. Parabola, 10. The Paper Puzzle Book.
I set a puzzle here every two weeks on a Monday. I'm always on the look-out for great puzzles. If you would like to suggest one, email me.