Question 170
A pile of stones is on a table, Pedrinho plays the following game: at each moment, he can choose a pile with at least 3 stones, remove one of these stones and divide the pile into two non-empty piles. For example, if he has a pile of 15 stones, he can divide this pile into two piles of 9 and 5 (he takes a stone, leaving 14 stones in the pile and then divides it). He can continue with the process. For example, Pedrinho can divide the pile with 9 stones into two, one of 3 and one of 5, leaving at the end with three piles, one of 3, and two of 5.
a) If at first there is a single pile with 19 stones on the table. Pedrinho manages, after a few movements, that all the remaining batteries have exactly 3 stones?
b) What if there is a single pile with 1001 stones?
a) If at first there is a single pile with 19 stones on the table. Pedrinho manages, after a few movements, that all the remaining batteries have exactly 3 stones?
b) What if there is a single pile with 1001 stones?