Question 5
Pedrinho chose 8 different numbers between 1 and 11 and wrote them in a certain order. Joãozinho, seeing the numbers that Pedrinho wrote, noticed the following curious fact: if we average the $n$ first numbers written by Pedrinho, $n=1, \ldots, 8$, we will always have an integer as a result. That is, if we average the first two numbers, the first three, the first four numbers, and so on, all these averages will be integers. What are the possible sequences of numbers that Pedrinho wrote? (Tip: First find out what the possible sums are for the 8 numbers, and then try to find out the chosen numbers backwards.)