The shopkeeper and the counterfeit note

Question

A customer buys goods worth 200 (the shopkeeper's own cost price) and pays with a 500 note. The shopkeeper has no change, so she takes the note to the neighbouring shop, gets five 100 notes, and gives the customer 300 in change plus the goods. Later the neighbour discovers the 500 note is counterfeit, and the shopkeeper repays him 500 in genuine money. How much has the shopkeeper lost in total? Answers of 300, 500, 700, 800 and 1,000 are all commonly given.

Accepted Answer

The shopkeeper lost 500: 300 in cash and 200 worth of goods. Follow the neighbour. The neighbour gave the shopkeeper 500 in genuine notes and later received 500 in genuine notes back. He is exactly square; he neither gained nor lost. Follow the counterfeiter. The customer handed over a worthless piece of paper and walked away with goods worth 200 and 300 in genuine cash. That is 500 of real value, and it all came from the shopkeeper, since the neighbour broke even. Why the other answers are wrong. Counting "300 change + 200 goods + 500 repaid to the neighbour = 1,000" double-counts: the 500 r…

The shopkeeper and the counterfeit note

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