11. What is the greatest 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 $a, \ldots, k$ is equal to 1 or -1?
93.11. Each of the six terms of the given sum is equal to 1 or -1, so this sum is even. It cannot take the value six, since in this case the terms $a e k, b f g, c d h$ must be equal to 1 and, therefore, their product is 1, and the terms $a f h, b d k, c e g$ must be equal to -1, and their product is -1. However, these products obviously coincide. The value 4 is achieved, for example, when $a=b=c=e=h=1, d=f=g=-1$.