Consider you have a collection of 10 coins. The coins can either be genuine or fake, a fake coin weights a slightly different amount than a genuine coin. All fake coins weigh the same and all genuine coins weigh the same. Using three measurements on a balance scale, prove either that all the coins have the same mass or that they do not.
For the balance scale rules, see the old counterfeit masses puzzle. These constant balance scale problems and total lack of hat problems are making me want to rename the blog "Standard Balance Scale Rules Apply".
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