### Brain Teasers

# Coin Story

Scatterbrain the Treasurer was a bit of a ... well, scatterbrain, and he had forgotten how many gold, silver and bronze coins were kept in the town vaults. So he decided to ask the three guards, each of whom guarded one type of coin, how many coins were in his charge. However, the guards were uncooperative, and the best that Scatterbrain could get from each was a statement about the numbers of coins in the other two vaults. Dimwit, who was guarding the gold, said there were 3000 silver and 5000 bronze coins; Thickplank, who was in charge of the silver, said there were 3000 gold and 5000 bronze; while Beefbrain, who was protecting the bronze, said there were 4000 gold and 3000 silver. Unfortunately, only one guard was being truthful, each of the other two stating at least one false amount. If there were 12000 coins altogether, how many of each type were there?

### Answer

There were 3000 gold coins, 4000 silver and 5000 bronze. Assume each statement to be true in turn and examine the consequences. If Dimwit is telling the truth, there are 3000 silver coins, 5000 bronze coins and hence 4000 gold coins. However, this would make Beefbrain's statement true also. By symmetry if Beefbrain is truthful so is Dimwit. Only if Thickplank is telling the truth are the other statements false.Hide Answer Show Answer

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