Suppose you have 30 coins identical in every way except one is either slightly lighter or slightly heavier than the other 29 coins. You can not find this difference by mere perception. You have a balance beam scale to weigh coins against each other. Using it only 4 times, can you figure out which is the counterfeit coin and whether it is lighter or heaver than all the other coins?

Suppose you have 30 coins identical in every way except one is either slightly lighter or slightly heavier than the other 29 coins. You can not find this difference by mere perception. You have a balance beam scale to weigh coins against each other. Using it only 4 times, can you figure out which is the counterfeit coin and whether it is lighter or heaver than all the other coins?

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