Problems

Age
Difficulty
Found: 2

Peter has 28 classmates. Each 2 out of these 28 have a different number of friends in the class. How many friends does Peter have?

In the country of Mara there are several castles. Three roads lead from each castle. A knight left from one of the castles. Traveling along the roads, he turns from each castle standing in his way, either to the right or to the left depending on the road on which he came. The knight never turns to the side which he turned before it. Prove that one day he will return to the original castle.