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You have 12 identical ball one of which is heavier OR lighter than and the rest (you don't know which). Using just a balance and 3 measurements, how can you determine which is the defective ball?

Hint: first do it for 9 identical balls and using only 2 measurements knowing that one is heavier (or lighter) than the rest.

Answer:

The solution to this one is very lengthy to write down. It starts by dividing the balls into 3 groups of 4 and comparing any two groups together. There are two possible outcomes: they balance, so the odd ball is the third group of 4 ball; or, they don't balance. Therefore, the odd ball is in one of the 8 on the balance (harder), but at least we have a identified four balls we know are non defective to determine if the ball is heavier or lighter in the next two measurements. Extra information is needed to be gather by noting any changes in direction of the balance when moving balls about for subsequent measurements to solve this problem.

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