Problem
COM-B1-M11-P003 Pluses and Minuses
#3
★☆☆☆☆ Level 1 of 5
There are \(8\) plus signs on a board. In one move, the signs of two symbols are changed. Can exactly \(3\) minus signs be obtained?
Track the parity of the number of minus signs.
Initially there are \(0\) minus signs. Changing two signs changes the number of minus signs by \(-2\), \(0\), or \(2\), so its parity is preserved. The number \(3\) is odd, so exactly \(3\) minus signs cannot be obtained.
Basic parity invariant.