There is a 100 × 100 square table
Source: Belarus IMO TST 1995 Day1 P1
November 28, 2015
combinatorics
Problem Statement
There is a 100 x100 square table, a real number being written in each cell. and play the following game. They choose, turn by turn, some row of the table (if it has not been chosen before). When and have rows chosen each, they sum the numbers in the corresponding cells of the chosen rows, and then sum the squares of all obtained numbers and compare the results. player who has the greater result wins. Player begins. Show that can avoid a defeat.