Another very nice puzzle I read on gurmeet.net/puzzles/, which as I have mentioned before, has a set of very nice mathematical puzzles.
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?
As always, please send your answers directly to me at firstname.lastname@example.org. If you like the puzzle, please share it with others. If you have interesting puzzles to share, please send them to me at my e-mail given above.