Question 61
Consider the set of 5-tuples of positive integers at most $5$. We say the tuple $(a_{1}, a_{2}, a_{3}, a_{4}, a_{5})$ is perfect if for any distinct indices $i, j, k$, the three numbers $a_{i}, a_{j}, a_{k}$ do not form an arithmetic progression (in any order). Find the number of perfect 5-tuples.