MathDB

2

Part of 1993 Brazil National Olympiad

Problems(1)

Real numbers on a chessboard

Source: Problem 2, Brazil MO 1993

3/18/2006
A real number with absolute value less than 11 is written in each cell of an n×nn\times n array, so that the sum of the numbers in each 2×22\times 2 square is zero. Show that for odd nn the sum of all the numbers is less than nn.
linear algebramatrixabsolute valuealgebra proposedalgebra