Suppose you have 12 coins identical in every way except one is either slightly more or slightly less than the other 11 coins. You can not tell this different by hand. You have a balance beam scale to weigh coins against each other but you may only use it 3 times. Using only 3 tries on the scale, how can you figure out which is the counterfeit coin AND tell whether it is lighter and heaver than all the other coins?
Suppose you have 12 coins identical in every way except one is either slightly more or slightly less than the other 11 coins. You can not tell this different by hand. You have a balance beam scale to weigh coins against each other but you may only use it 3 times. Using only 3 tries on the scale, how can you figure out which is the counterfeit coin AND tell whether it is lighter and heaver than all the other coins?
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