## Puzzle #91: Pebble Piles

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 alokgoyal_2001@yahoo.com. 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.

Happy pebbling!

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### 1 Response to Puzzle #91: Pebble Piles

1. Amit Mittal says:

I use 25s. so 51 49 5 become 100 5 >> 50 50 5 >> 25 25 25 25 5

From there the 5 makes one 25 30 >> 25 25 25 15 15

which similarly 25 25 20 20 15 and the 20s become 5s the other 15 complements the 25 for Operation 1 again and thats 20 20 20 20 25 or 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 25 and the last 5 pairs 25 to become 30 to two 15s which use another two 5s and so on, making everything 5s

that stops at 5 primes so i cannot get to less than 5s in this “synchronous” operation.

so i think i need two odd series and not everything the same , 49 5 gives 27s which give 3s or 51 5 gives 28s which gives 7s , and then i give up, lol 🙂 happy hunting!