2. Three piles of stones, one with 51 stones, another with 49 stones, and the last with 5 stones. Any two piles can be combined into one pile. Also, a pile with an even number of stones can be divided into two piles of equal number of stones. Can these two steps be used to transform the three piles into 105 piles, each with one stone?
2. Impossible.

Due to the first step having three scenarios:
(i) $(51,49.5) \rightarrow(100.5)$ are all multiples of 5;
(ii) $(51,49,5) \rightarrow(51,54)$ are all multiples of 3;
(iii) $(51.49 .5) \rightarrow(56,49)$ are all multiples of 7.

In summary, according to the two steps given in the problem, a parent pile with a count of 1 will never be produced at any time.