Brain Teaser

(from miltownkid with variation)

You are given 12 coins which all look exactly the same. One of them is a counterfeit coin and will be either lighter or heavier depending on what it was made from. Using a balancing scale, take exactly 3 measurements to find the counterfeit coin and determine if it is lighter or heavier than normal.

Balancing Scale

The big variation is that miltownkid’s version didn’t require you to also determine whether the odd item is heavier or lighter, just to find the one which was different. (This version is written more like a story too.) I solved his version in just about three hours but had one particular case where it was undetermined if the weight is heavier or lighter. Having to find that makes it just a bit more complicated. (My solution was also a bit more complex than the canonical solutions available online. (No peeking!))

This one looks easy, and you’ll think you are on the right track about a dozen times before you actually get it. Keep checking that all possible cases can work out in only three measurements. If you solve it, send me an email rather than putting a spoiler in the comments.

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