105 Piles of Pebbles
Source: Fall 2007 Tournament of Towns Senior P-Level #4
March 31, 2015
number theorycombinatoricsinvariant
Problem Statement
There three piles of pebbles, containing 5, 49, and 51 pebbles respectively. It is allowed to combine any two piles into a new one or to split any pile consisting of even number of pebbles into two equal piles. Is it possible to have 105 piles with one pebble in each in the end?(3 points)