Problem: You are given three piles with 5, 49 and 51 pebbles respectively. Two operations are allowed:
(a) merge two piles together or
(b) divide a pile with an even number of pebbles into two equal piles.
Is there a sequence of operations that would result in 105 piles with one pebble each?
Solution: Posted by Shantanu Gangal (CSE IITB Alumnus and BCG Consultant) in comments!!