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**1. Homework Statement**

The sum of 8 positive integers is 31. If no individual integer value can appear more than twice in the list of 8 integers, what is the greatest possible value that one of the integers can have?

**2. Homework Equations**

?

**3. The Attempt at a Solution**

My answer is 16. I did a lot of calculating; a lot of trial and error.

I doubled 3 of the lowest possible numbers, which totaled 6. I used 6 numbers; there are 2 left.

0+0=0

1+1=2

2+2=4

16+6=22 (7 numbers have been used)

22+9=31 (all 8 numbers have been used)

17 would be too high, even if the lowest possible numbers are used. 16 is the highest possible number.

How do I formulate the equation to solve this problem?

Is 16 the correct answer?