A classic cash register brain teaser asks a deceptively simple question: if a person takes a $100 bill from a shop, then uses that same bill to buy $70 in merchandise and receives $30 in change, how much does the shopkeeper lose?
The correct answer is $100.
This puzzle is often shared as a test of mental math, financial reasoning, and attention to detail. Although several dollar amounts appear in the scenario, adding them all together produces an incorrect result because it counts the same $100 bill more than once. The key is to track the shopkeeper’s final position after every part of the transaction has occurred.
By looking separately at cash and merchandise, the answer becomes clear: the shopkeeper ends up losing $70 worth of goods and $30 in cash. Together, those losses equal $100.
The Classic $100 Shopkeeper Puzzle
Here is the scenario in straightforward terms:
- A person enters a shop and takes a $100 bill from the cash register without permission.
- The person then selects $70 worth of merchandise.
- The same $100 bill is handed to the shopkeeper as payment.
- The shopkeeper accepts the bill, not realizing it is the same money that was taken earlier.
- The shopkeeper gives the customer $30 in change.
At first, it may seem that the shopkeeper loses $200, because the situation includes a stolen $100 bill, $70 in merchandise, and $30 in change. That calculation is not correct. The $100 bill returns to the register during the purchase, so it is no longer missing when the transaction is complete.
The final loss is not based on every amount mentioned in the story. It is based on what the shopkeeper no longer possesses at the end: $70 in merchandise and $30 in cash.
The Correct Answer: The Shopkeeper Loses $100
After the full sequence is finished, the original $100 bill is back in the cash register. Therefore, the shopkeeper does not have a final loss of that particular bill.
However, two things are gone:
- $70 worth of merchandise leaves the shop with the customer.
- $30 in cash leaves the register as change.
The total is:
$70 + $30 = $100
Therefore, the shopkeeper’s total loss is $100.
Why the Stolen $100 Bill Should Not Be Added Again
The most common mistake in this puzzle is treating the original $100 bill as a separate final loss. It is understandable why people do this: the bill was initially taken from the register, so it appears to create a $100 loss.
But the person later uses that exact bill to make a purchase. Once the shopkeeper receives it back, the register is restored to its original cash position before the merchandise sale and change payment are considered.
In other words, the bill is temporarily absent, but it is not absent at the end of the scenario. Counting it as a loss after it has returned is an example of double-counting.
A useful way to approach the question is to ignore the middle of the story for a moment and compare the shopkeeper’s inventory and cash before and after the event.
