## Non-Transitive Dice

This is a non-transitive dice set, i.e. every dice in it is weaker than some other dice. Can you design a non-transitive set with only 3 dice?

Remark: “Weaker” means that it loses more often than it wins.

The simplest solution is given by:

2, 2, 4, 4, 9, 9;
1, 1, 6, 6, 8, 8;
3, 3, 5, 5, 7, 7.

Another solution is given by the so-called “Miwin’s dice”. They are as follows:

1, 1, 3, 5, 5, 6;
2, 3, 3, 4, 4, 5;
1, 2, 2, 4, 6, 6.

## Socks in the Drawer

You have a drawer with 10 pairs of black socks and 10 pairs of white socks. How many times do you need to blindly reach inside the drawer and take out a sock, so that you get a matching pair?

Only 3 times. Once you have two socks of the same color, they already form a matching pair.

## Seven Sevens

Seven sevens are given. Find the other digits in this multiplication.

21817 x 96787 = 2111601979

## Rich and Poor

Who is richer – the richest among the poor or the poorest among the rich?

The poorest among the rich is richer than the richest among the poor. That is because any rich person is by default richer than any poor person.

## Prank the Professors

Three professors fell asleep under a tree. At some point a prankster passed by and painted their faces with black dye. When the professors woke up, each of them saw the others’ faces and started laughing at them. After a while though, they stopped laughing, realizing that their own faces were painted as well. How did they deduce that?

Let us denote the professors with A, B and C. The thought process of A would go like this: “If my face is not painted, then B will see that C is laughing at him and will realize immediately that he is being pranked. However, B was laughing for a while and therefore my I must being pranked as well.”. Then A will stop laughing and the same will happen with the other two professors B and C.