Question 10
We have two boxes of balls, containing $m$ and $n$ balls, where $m,n\gt 0$. Two operations are allowed:
(i) Remove the same number of balls from each box.
(ii) Multiply the number of balls in one box by $k$.
Is it always possible to empty both boxes using these operations,
a) if $k=2$?
b) if $k=3$?
(i) Remove the same number of balls from each box.
(ii) Multiply the number of balls in one box by $k$.
Is it always possible to empty both boxes using these operations,
a) if $k=2$?
b) if $k=3$?