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?
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.
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?