The King's Horses

In your book, Maths Mela (Chapter 1), there is a story called 'King's Horses'. Once upon a time a king who loved horses had 20 horses of the best breed. They lived in a royal stable, looked after by a caretaker. One night a thief stole one horse. The caretaker was afraid of being punished, so he moved the 19 horses around in the stable.

The stable is square, with rooms all along its four sides and an open yard in the middle. Each side has 4 rooms, and the room at each corner belongs to TWO sides at once. In the caretaker's arrangement, the top side had 1 horse in its left corner room, then 2, then 2, and none in its right corner room: 5 horses. The left side had that same corner horse, then 1, then 3, and an empty corner: 5 horses. The right side and the bottom side had 2 and 3 in their middle rooms and empty corners: 5 horses each.

The next day the caretaker led the king around and asked him to count the horses along each side. The king counted 5 on every side. 'We have 5 horses along each side and there are 4 sides, so there are 20 horses, Your Majesty,' said the caretaker. The king was satisfied and went back to his palace.

But count the horses one by one: 1 + 2 + 2 in the top row, 1 + 3 on the left, 2 + 3 on the right and 2 + 3 at the bottom make 19. What was the trick? The horse in the corner room is on the top side AND on the left side, so the king counted it twice. Every horse in a corner is counted on two sides. So 5 + 5 + 5 + 5 = 20 is only right when no horse stands in a corner.

The next night the thief stole another horse, leaving 18. The caretaker again showed 5 on each side. This time 2 horses had to be in corner rooms, so that 2 horses were counted twice: 18 + 2 = 20.