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sum of products not zero

Source: Greek MO 2007

March 5, 2007

combinatorics unsolvedcombinatorics

Problem Statement

Given a

2007\times 2007

array of numbers

1

and

-1

, let

A_{i}

denote the product of the entries in the

i

th row, and

B_{j}

denote the product of the entries in the

j

th column. Show that

A_{1}+A_{2}+\cdots +A_{2007}+B_{1}+B_{2}+\cdots +B_{2007}\neq 0.

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