Find the maximum value that the expression $a e k-a f h+b f g-b d k+c d h-c e g$ can take if each of the numbers $a, b, c, d, e, f, g, h, k$ is equal to $\pm 1$.

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Evaluation. The product of all addends equals - $(a b c d e f g h k)^{2}$, which is negative. Therefore, the number of minus ones among the addends is odd and thus not equal to zero. Consequently, the sum does not exceed 4.

Example. Let $a=c=d=e=g=h=k=1, b=f=-1$. Then the given expression equals 4.

## Answer

4.