The sum of <strong>ALL</strong> possible products taken two at a time out of the numbers \pm1, \pm2, \pm3, \pm4, \pm5 is

Explanation

Use the identity (\sum x_i)^2 = \sum x_i^2 + 2 \sum(x_i x_j). The sum of the numbers is 0. The sum of their squares is 2 \times (1^2+2^2+3^2+4^2+5^2) = 2 \times 55 = 110. Thus, 0^2 = 110 + 2S \Rightarrow S = -55.

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