Piglet has 10 cans of milk. In this game, there are 100 coins on one scale, and 200 coins on another scale. Each of two players in turn takes one or more of the coins from one of the scales. The player who makes the number of coins on the two scales equal loses. Scrooge and Glomgold play a game.
Scrooge makes the first move.
Begin with 1 on the calculator, and prove that it is impossible to arrive at an answer of 2 when using exactly 1996 operations. In a tribe of cannibals there are 20 persons. Each person likes some of his or her fellow-tribesmen and does not like others. Each day all of the people who are liked by more than half the tribe become dinner. Prove that on the 10th day after the first cannibal has been eaten, because no person is liked by more than half of the other cannibals there is no dinner.