Problem
COM-B1-M06-P006 Product of Signs
#6
★★☆☆☆ Level 2 of 5
There are \(7\) plus signs on the board. In one move, exactly two signs are changed. Can all signs become minus?
The product of all signs is preserved.
Changing two signs multiplies the product by \((-1)^2=1\). Initially the product is \(+1\). With \(7\) minuses, the product is \(-1\). Impossible.
The product is sometimes more convenient than counting minuses.