Product game
Source: JBMO Shortlist 2002
November 12, 2008
combinatorics proposedcombinatorics
Problem Statement
A student is playing computer. Computer shows randomly 2002 positive numbers. Game's rules let do the following operations
- to take 2 numbers from these, to double first one, to add the second one and to save the sum.
- to take another 2 numbers from the remainder numbers, to double the first one, to add the second one, to multiply this sum with previous and to save the result.
- to repeat this procedure, until all the 2002 numbers won't be used.
Student wins the game if final product is maximum possible.
Find the winning strategy and prove it.