How Much Did the Shop Lose in the Stolen-Money Riddle?

The usual version of the stolen-money riddle has a thief take a $100 bill from a shop, then use that same bill to pay for$70 worth of goods. The shopkeeper gives the thief $30 in change. The shop’s loss is **$100**, using the goods’ selling price: $70 in goods and$30 in change.

The apparent puzzle comes from counting the stolen bill twice. Once the shop receives that same bill back as payment, it is no longer missing from the cash drawer. What remains missing is the change and the merchandise.

Follow the bill and the goods

Assume the bill is genuine, the shop accepts it, and the stated $70 is the merchandise’s selling price. Track the events one at a time:

Event	Change to the shop
Thief takes $100 from the cash drawer	−$100 cash
Thief pays with that same $100 bill	+$100 cash
Shop gives $30 change	−$30 cash
Shop hands over $70 worth of goods	−$70 in goods, at selling price

The two cash movements involving the $100 bill cancel: the shop loses the bill, then gets it back. The remaining cash loss is$30. Add the $70 of goods that have left the shop, and the loss at the goods’ selling price is$100.

In symbols:

$$\text{loss} = \text{change} + \text{goods at selling price} = 30 + 70 = 100.$$

Why $200 is the wrong answer

A tempting calculation is to add the stolen $100 to the$70 of goods and $30 of change. That gives$200, but it treats the original bill as missing even after the shop receives it back.

The sequence matters. The thief’s payment is not a second, unrelated $100 bill in addition to the stolen bill; it is the stolen bill returning to the shop. Count each cash movement once, and count the goods that leave the shop once.

Another way to check the result is to compare the shop’s position before and after the whole episode. The shop ends with $30 less cash in the drawer and$70 less merchandise at its selling price. Together, those are $100 of value.

Does the shop always lose exactly $100?

The standard puzzle treats the goods as worth their $70 selling price, so its intended answer is$100. In real bookkeeping, “loss” can depend on how the merchandise is valued. If the shop paid $40 for the goods, for example, those goods may be recorded as a$40 inventory asset rather than $70. On that cost basis, the shop’s decrease in cash and inventory is$30 + $40 =$70.

That cost-based figure answers a different accounting question from the riddle’s usual one. The shop records a $70 sale and suffers a$100 cash theft; with goods costing $40, the combined change in cash and inventory is a decrease of$30 + $40 =$70. The $100 riddle answer instead values the goods at their$70 selling price. Unless the problem gives the goods’ cost and specifies an accounting measure, use the selling-price convention and answer $100.

Common mistakes

• Counting the $100 bill twice: It leaves the drawer during the theft but comes back as the thief’s payment.
• Counting only the $30 change: That ignores the merchandise given away.
• Adding the $100 theft to the whole purchase again: The theft and payment are linked because the same bill is used in both events.
• Mixing selling price and cost: Use one valuation consistently. The classic riddle uses the $70 selling price; a cost-based accounting calculation needs the merchandise’s actual cost.

If a version of the riddle changes the amounts, use the same method: track whether the stolen money is returned, then add the cash and goods that are still gone.