Frogs game
Source:
June 8, 2008
combinatorics proposedcombinatorics
Problem Statement
There are 2008 bags numbered from 1 to 2008, with 2008 frogs in each one of them. Two people play in turns. A play consists in selecting a bag and taking out of it any number of frongs (at least one), leaving frogs in it (). After each play, from each bag with a number higher than the selected one and having more than frogs, some frogs scape until there are frogs in the bag. The player that takes out the last frog from bag number 1 looses. Find and explain a winning strategy.