An artist paints two congruent dragons on two congruent circular paper discs. The center of the first disc coincides with one of the drago's eyes, which is not the case with the second disc. Prove that the second disc can be cut into two pieces from which a disc of the same radius can be assembled, containing the same dragon, but so that his eye coincides with the center of the new disc.

A row of minuses is written on a blackboard. Two players take turns in replacing either a single minus by a plus or two adjacent minuses by pluses. The one who cannot make a move loses. Can the player who starts force a win?

Several weights are given, each of which is not heavier than 1 lb. It is known that they cannot be divided into two groups such that the weight of each group is greater than 1 lb. Find the maximum possible total weight of these weights.

In a parliament, each parliamentarian has at most three enemies. Prove that the parliament can be divided into two chambers in such a way that no parliamentarian has more than one enemy in his or her chamber.

The two-move chess game has the same rules as the regular one, with only one exception: each player has to make two consecutive moves at a time. Prove that White (who goes first) has a nonlosing strategy.