Problem
COM-B1-M06-P017 Signed Sum
#17
★★★☆☆ Level 3 of 5
Can signs \(+\) and \(-\) be placed before \(1,2,\ldots,10\) so that the sum becomes \(0\)?
Look at the parity of the sum.
The sum \(1+2+\cdots+10=55\) is odd. Changing the sign of \(a\) changes the sum by \(-2a\), an even number. Thus the parity of the sum remains odd. Zero is even, so it is impossible.
Parity invariant of a signed sum.