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Is it possible to fill in the blanks below with $+$ and $-$ signs to create a total of $20$?  $1 $\_$ 2 $\_$ 3 $\_$ 4 $\_$ 5 $\_$ 6 $\_$ 7 $\_$ 8 $\_$ 9$ In this case, we find that such a construction is not possible. Here, we have $5$ odd numbers and therefore the total must be odd. Since $20$ is even, this proves it cannot be done.