350. Three integers were written on the board. Then one of them was erased and replaced with the sum of the other two remaining numbers, decreased by one. This operation was repeated several times, and as a result, the numbers 17, 1967, 1983 were obtained. Could the numbers originally on the board have been: a) $2,2,2 ;$ b) $3,3,3$?
350. Answer: a) no; b) yes.

It is useful to reason "from the end": the triplet ( $17,1967,1983$ ) could only have been obtained from the triplet ( $5,3,3$ ), and the triplet $(5,3,3)$ results from the triplet ( $3,3,3$ ) and does not result from the triplet $(2,2,2)$.