Enigma 1606: Nightmare!
4 January 2012
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From New Scientist #2771, 31st July 2010 [link]
You are in a locked room, seated at a table on which stands a two-pan balance. One of the pans holds a number of steel ball bearings, each weighing the same whole number of grams greater than 1.
If you could determine the total weight of the balls, you could work out the number of balls there are. This number is particularly important to you as it is the same number as the combination security lock on the door.
Next to the balance is a set of weights, each weighing the same whole number of grams, and together totalling 4 kilograms. If you were allowed to use the balance, these would enable you to work out the weight of the balls. But if you disturb the balance, in any way, it will explode catastrophically.
Thankfully, with those particular weights you already have all the information you need to work out the number of balls with absolute certainty.
What number opens the security lock and grants your freedom?