The Great Sultan of the Indies was sent by one of his viziers 99 bags of gold, each containing exactly 50 coins. Hidden somewhere in those 99 bags is a hollowed coin (indistinguishable to the naked eye from the others) containing a secret message destined to His Most Excellent Majesty. Using a simple two-pan balance, in how many weighing can you find the bag containing the lighter coin? With how many further weighing can you find the coin within the bag?

The solution of the problem is not that complicated, but depends entirely on the assumptions you make on the balance. If one supposes that the balance is large enough to pile the 99 bags in either one of its pan, and that is locked while you’re loading it, giving its reading only once you’re done loading it, the solution that comes to mind is Read the rest of this entry »