MathDB

22

Part of 1971 IMO Longlists

Problems(1)

The old +1 and -1 problem on the board - [IMO LongList 1971]

Source:

1/1/2011
We are given an n×nn \times n board, where nn is an odd number. In each cell of the board either +1+1 or −1-1 is written. Let aka_k and bkb_k denote them products of numbers in the kthk^{th} row and in the kthk^{th} column respectively. Prove that the sum a1+a2+⋯+an+b1+b2+⋯+bna_1 +a_2 +\cdots+a_n +b_1 +b_2 +\cdots+b_n cannot be equal to zero.
modular arithmeticinvariantcombinatorics proposedcombinatorics