Question 153
$1019$ stones are placed into two non-empty boxes. Each second Alex chooses a box with an even amount of stones and shifts half of these stones into another box.
Prove that for each $k$, $1 \le k \le 1018$, at some moment there will be a box with exactly $k$ stones.
Prove that for each $k$, $1 \le k \le 1018$, at some moment there will be a box with exactly $k$ stones.