Problem #PRU-100388

Problems Number Theory Arithmetic operations. Number identities Discrete Mathematics Algorithm Theory Game theory Winning and loosing positions

Problem

Assume you have a chance to play the following game. You need to put numbers in all cells of a \(10\times10\) table so that the sum of numbers in each column is positive and the sum of numbers in each row is negative. Once you put your numbers you cannot change them. You need to pay £1 if you want to play the game and the prize for completing the task is £100. Is it possible to win?