Negativ product
Write exactly one real number into each cell of a grid.
Is it possible that the product of the 2017 numbers in any row is positive, and the product of the 2017 numbers in any column is negative?
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1 solution
Assume that it is possible. Let S be the product of the numbers in the square.
We can get S in two ways:
1) We calculate the 2 0 1 7 number's product in each row, and then multiply the products.
2) We calculate the 2 0 1 7 number's product in each column, and then multiply the products.
In the 1) way we multipled 2 0 1 7 positive numbers, so S is positive. In the 2) way we multipled 2 0 1 7 negativ numbers, so S is negativ. Hence S is positive and negativ too, which is a contradiction.
Therefore it is not possible.