2. The gnomes have gone to work, and Snow White is feeling lonely. She laid out a pile of fifteen stones on the table. Every minute, Snow White splits one pile into two non-empty piles and adds a stone to one of them. How can Snow White use these actions to get seven identical piles?
Solution. First, let's understand how many stones are in the piles. With each action, the number of piles increases by one, as does the number of stones. Therefore, 7 piles will arise after 6 actions, with the total number of stones being $15+6=21$. This means each pile should have three stones. From these considerations, it is easy to construct an example - each time, the largest pile should be split into $3+X$, and a stone should be added to $X$:

$15-313-3311-3339-333337-3333335-3333333$

Note: Other sequences of actions are possible, but if an even number arises at any point, the example will not converge, as splitting an even pile always results in piles of different parity (and, thus, unequal size)