4

Part of 2007 Greece National Olympiad

Problems(1)

sum of products not zero

Source: Greek MO 2007

2007\times 2007

array of numbers

1

-1

A_{i}

denote the product of the entries in the

i

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.

combinatorics unsolvedcombinatorics