2012 ToT Spring Senior A p7 a pile of 100 pebbles
Source:
March 5, 2020
combinatorics
Problem Statement
Konstantin has a pile of pebbles. In each move, he chooses a pile and splits it into two smaller ones until he gets piles each with a single pebble.
(a) Prove that at some point, there are piles containing a total of exactly pebbles.
(b) Prove that at some point, there are piles containing a total of exactly pebbles.
(c) Prove that Konstantin may proceed in such a way that at no point, there are piles containing a total of exactly pebbles.