Answer to Question #311 in Algebra for Ken

Question

Is it possible to put plus and minus signs instead of asterisks in the equation 1 ∗ 2 ∗ 3 ∗ … ∗ 10 = 0 to obtain a true equality?

Answer 1

No. The parity of the number 1 ± 2 ± 3 ± ⋯ ± 10 doesn’t depend on the signs selection; it depends only on the amount of odd numbers in the expression. There are 5 odd numbers in the given expression, thus the result will always be an odd number.