Question 9
Let $S$ be the set of all ordered triples of integers $(a_1, a_2, a_3)$ with $1 \le a_1,$ $a_2,$ $a_3 \le 10.$ Each ordered triple in $S$ generates a sequence according to the rule $a_n = a_{n-1} \cdot |a_{n-2} - a_{n-3}|$ for $n \ge 4.$ Find the number of such sequences for which $a_n = 0$ for some $n.$