Question 23
Three positive integers are written on a blackboard. A move consists of replacing one of the numbers by the sum of the other two less one. For example, if the numbers are $3$, $4$, $5$, then one move could lead to $4$, $5$, $8$ or $3$, $5$, $7$ or $3$, $4$, $6$. After a series of moves the three numbers are $17$, $1967$ and $1983$. Could the initial set have been $2$, $2$, $2$? $3$, $3$, $3$?