Weighing piles of coins

[I got this puzzle from Dave Detlefs, who read it in an MIT Alumni magazine. This puzzle is a bit more involved than most puzzles on my page, so you may want a paper and pen (and some tenacity) for this one. Once you get into it, though, it’s a hard puzzle to put aside until you’ve solved it.]

There are two kinds of coins, genuine and counterfeit. A genuine coin weighs X grams and a counterfeit coin weighs X+delta grams, where X is a positive integer and delta is a non-zero real number strictly between -5 and +5. You are presented with 13 piles of 4 coins each. All of the coins are genuine, except for one pile, in which all 4 coins are counterfeit. You are given a precise scale (say, a digital scale capable of displaying any real number). You are to determine three things: X, delta, and which pile contains the counterfeit coins. But you’re only allowed to use the scale twice!

January 2010

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