18*. Each of the variables $a, b, c, d, e, f$ is defined on the set of numbers $\{1; -1\}$. On which set is the variable $x$ defined, if $x=a-b+c-d+e-f$?
18. Solution. The maximum value of the sum is 6, and the minimum is -6. When the sign of any number is changed, the sum changes by 2. Therefore, the sum can only take one of the following values: $\{-6; -4; -2; 0; 2; 4; 6\}$. It is not difficult to provide examples confirming that the sum can take each of these values.