MathDB
numbers 1-2^{1998} in 1999 cells {- All-Russian MO 1998 Regional (R4) 10.4

Source:

September 17, 2024
combinatoricsnumber theorypower of 2

Problem Statement

In the first 19991999 cells of the computer are written numbers in the specified order:: 11, 22, 44,...... , 219982^{1998}. Two programmers take turns reducing in one move per unit number in five different cells. If a negative number appears in one of the cells, then the computer breaks down and the broken repairs are paid for. Which programmer can protect himself from financial losses, regardless of his partner’s moves, and how should he do this act?