They start with 10 dots on a sheet of paper and, taking turns, connect any two of them which are not already connected. The first player to make the resulting graph connected loses.

A father left to his four sons this square field, with the instruction that they divide it into four pieces, each of the same shape and size, so that each piece of land contained one of the trees. How did they manage it?

Napoleon has landed on a deserted planet with only two policemen on it. He is traveling around the planet, painting a red line as he goes. When Napoleon creates a loop with red paint, the smaller of the two encompassed areas is claimed by him. The policemen are trying to restrict the land Napoleon claims as much as possible. If they encounter him, they arrest him and take him away. Can you prove that the police have a strategy to stop Napoleon from claiming more than 25% of the planet’s surface?

We assume that Napoleon and the police are moving at the same speed, making decisions in real time, and fully aware of everyone’s locations.

SOLUTION

First, we choose an axis, so that Napoleon and the two policemen lie on a single parallel. Then, the strategy of the two policemen is to move with the same speed as Napoleon, keeping identical latitudes as his at all times, and squeezing him along the parallel between them.

In order to claim 25% of the planet’s surface, Napoleon must travel at least 90°+90°=180° in total along the magnitudes. Therefore, during this time the policemen would travel 180° along the magnitudes each and catch him.

A long time ago there was a kingdom, isolated from the world. There was only one way to and from the kingdom, namely through a long bridge. The king ordered the execution of anyone caught fleeing the kingdom on the bridge and the banishment of anyone caught sneaking into the kingdom.

The bridge was guarded by one person, who was taking a 10-minute break inside his cabin every round hour. Fifteen minutes were needed for a person to cross the bridge and yet, one woman managed to escape the kingdom. How did she do it?

SOLUTION

Once the guard entered the cabin, the woman started crossing the bridge for 9 minutes, and then turned around and pretended to be going in the opposite direction for one more minute. When the guard caught her, she said she was trying to enter the kingdom, so he banished her away.

In the position below, Black played a move, but right before he pressed the clock, he ran out of time. However, the judge declared a draw instead of awarding a victory to the opponent. Why?

SOLUTION

The rules of FIDE state that if a player runs out of time, their opponent wins the game IF they have a path to victory. If there is no sufficient material, e.g. a King and a Knight against a King, then the game is declared a draw.

In this position, Black played Rxg6 which forces the moves:

… Rxg6+

Nxg6+ Rxg6+

Kxg6+ Qxg6+

Kxg6

This leaves White with a King and a Knight against Black’s King. Thus, White did not have a path to victory and the game was declared a draw.

A man is found unconscious in front of a store at two in the morning. His head is bleeding and there is a brick laying next to him. When the police arrive, they carry the man to jail. Why did they arrest him?

SOLUTION

The man was a burglar who tried to break the store’s glass with the brick. The glass turned out to be bullet proof, so the brick bounced back and hit him in the head, knocking him out.

There are 7 loaves of bread that need to be shared equally among 12 people. How would you do this if you are not allowed to split any loaf into 12 pieces?

SOLUTION

Split 4 of the loaves into 3 pieces and the other 3 loaves into 4 pieces. Then, give each person one of both types of pieces.