Pooh and Piglet cooperate against Rabbit
Source: All-Russian MO 1999
December 31, 2012
combinatorics unsolvedcombinatoricsGame Theory
Problem Statement
There are three empty jugs on a table. Winnie the Pooh, Rabbit, and Piglet put walnuts in the jugs one by one. They play successively, with the initial determined by a draw. Thereby Winnie the Pooh plays either in the first or second jug, Rabbit in the second or third, and Piglet in the first or third. The player after whose move there are exactly 1999 walnuts loses the games. Show that Winnie the Pooh and Piglet can cooperate so as to make Rabbit lose.