IMO 1971 LL HUN22

We are given an n imes n board, where n is an odd number. In

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IMO 1971 LL HUN22

Origin: HUN

Problem

We are given an n \times n board, where n is an odd number. In each cell of the board either +1 or −1 is written. Let ak and bk denote the products of numbers in the kth row and in the kth column respectively. Prove that the sum a1 + a2 + \cdot \cdot \cdot + an + b1 + b2 + \cdot \cdot \cdot + bn cannot be equal to zero.