From Henry Dudeney:
A banker in a country town was walking down the street when he saw a five-dollar bill on the curb. He picked it up, noted the number, and went to his home for luncheon. His wife said that the butcher had sent in his bill for five dollars, and, as the only money he had was the bill he had found, he gave it to her, and she paid the butcher. The butcher paid it to a farmer in buying a calf, the farmer paid it to a merchant who in turn paid it to a laundry woman, and she, remembering that she owed the bank five dollars, went there and paid the debt.
The banker recognized the bill as the one he had found, and by that time it had paid twenty-five dollars worth of debts. On careful examination he discovered that the bill was counterfeit. What was lost in the whole transaction, and by whom?
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“Since the identical counterfeit bill can be traced through all the transactions, these are all invalid. Therefore everybody stands in relation to his debtor just where he was before the banker picked up the note, except that the butcher owes, in addition, $5.00 to the farmer for the calf received.”
Update: A number of perceptive people have written in questioning Dudeney’s solution, and after some thought I’m inclined to agree with them. The intermediate transactions can stand as they are: Each participant has lost $5 (by accepting a fake bill) and gained $5 (by using it to pay a debt). But the banker has gained $5 (by finding and spending a bad bill), and the bank has lost $5 (by accepting it as good). So if the banker now pays $5 to the bank, all is well.
This puzzle first appeared in The Strand in 1917, and it’s appeared in various collections since then, but I have not seen these objections raised until now. This means I have the best readers in the world.