8.72 On the blackboard, 3 integers were written, then one of them was erased and replaced with the difference between the sum of the remaining two numbers and 1. After repeating this step several times, the numbers on the blackboard became $17,1967,1983$. Could the numbers initially written on the blackboard have been the following sets:
(1) $2,2,2$;
(2) $3,3,3$?
[Solution] Tracing back from $(17,1967,1983)$ is convenient. Each time the largest number is removed, the remaining two numbers can both decrease by 16. Since $1983=123 \times 16+15$, we can deduce $(15,17,31),(3,15,17)$. Each time the largest number is removed, the remaining two numbers can decrease by 2, thus finally obtaining $(3,3,5)$. This set can be derived from $(3,3,3)$ but not from $(2,2,2)$.