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12-Ball riddle
Just saw a riddle that people appear to find rather difficult:
[Quote:]
You have 12 small balls. All look exactly the same, and weigh exactly the same; they are duplicates. But one of the balls is an exception: it is either lighter or heavier, but looks the same.
You are given a double-sided weighing machine (ie. counterweighing) to find out which ball is the exception, and whether it is lighter or heavier than the others. You have 3 uses of the weighing machine.
And thinking through made me realize that if you know the ball is lighter (instead of “lighter or heavier”) you can do the same puzzle with 27 balls. Feel free to put the answer in the comments, if you can find it…
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Ok, I give. How do you do it? I’ve been trying to figure it out, but I can’t think of it. I’m usually good with this stuff too.
Make three heaps, each nine balls. Weigh two heaps – if they’re equal, the lighter ball is in the third heap, if they’re not equal, take the lighter heap. Divide that heap in three heaps of three balls each, and repeat. Repeat again with the remaining three balls.