To find the answer to this question, we can approach it step by step:
1. Let's start by assigning a variable to represent the first integer. Let's call it "n".
2. Since we are looking for 8 consecutive integers, we can write the sum of these integers as follows:
n + (n+1) + (n+2) + (n+3) + (n+4) + (n+5) + (n+6) + (n+7) = 31
3. Simplifying this equation, we get:
8n + 28 = 31
8n = 31 - 28
8n = 3
4. Divide both sides of the equation by 8 to solve for "n":
n = 3/8
5. Since we are looking for integers, we need to check if 3/8 is an integer. However, we already know that only one integer is repeated in the sequence. Therefore, 3/8 cannot be an integer, and our assumption about the repetition was incorrect.
Given this information, we can conclude that the greatest number for any one integer is 7.