The sum of 8 one-digit positive integers is 68 . If seven of these integers are equal, determine the other integer.
Let $x$ be the one-digit integer that is included 7 times.

Since $x$ is at most 9 , then $7 x$ is at most 63 .

If $x=9$, then the other integer is $68-7 x=68-63=5$.

If $x \leq 8$, then $7 x$ is at most 56 , and so the other integer would have to be at least 12 , which is not possible since it is a one-digit integer.

Thus, the other integer is 5 .

ANSWER: 5