A simple question about a stolen $100 bill has confused more people than anyone expected. At first, it sounds easy. A man steals $100 from a store register, then returns to the same store and buys $70 worth of goods using that same $100 bill. The cashier gives him $30 in change, and the question becomes: how much money did the store actually lose?

Many people immediately say the store lost $200 because the thief stole $100 first, then took $70 in goods and $30 in change. Others argue the store only lost $100 because the stolen bill came back into the register. That is where the trick begins. The same $100 bill cannot be counted twice as a separate loss once it returns to the store.

The clean way to understand it is simple. The store first loses $100 from the register. Later, the thief gives that same $100 back while buying items. At that moment, the cash part is balanced again, but the store still gives away $70 worth of goods and $30 in change.

So the real loss is $100 total. That loss is made up of $70 in merchandise plus $30 in cash. The stolen bill returning to the register cancels out the original missing cash, but it does not cancel the goods and change the thief walked away with.

This is why the answer surprises people. The store did not lose $200, $170, or $130. It lost exactly $100, even though the situation feels more complicated than it really is.

One way to check the calculation is to write down the two cash movements separately. During the first visit, the register goes down by one hundred dollars. During the second visit, it goes up by one hundred dollars when the bill comes back. Those entries offset each other. The cashier then pays out thirty dollars, so the register ends with thirty dollars less than it held before either visit.

The shelf tells the rest of the story. The shopper leaves with items marked at seventy dollars, and the store receives no money that the shopper brought in from outside. The same bill is doing two jobs in the telling of the puzzle: first it is taken, and then it is handed back. A ledger records those as opposing movements. Counting the first withdrawal again after crediting the return would count the same money twice.

A second way to see the answer is to look at the shopper’s final position. The person starts without the store’s bill and ends without it, because it has gone back into the register. What remains in the shopper’s possession is thirty dollars in change and the goods. On the puzzle’s stated valuation, that adds up to one hundred dollars.

The merchandise is valued at its seventy-dollar sale price in the riddle. If the question instead asks how much cash and inventory cost the store on its own books, the cost of that inventory would have to be supplied separately. The puzzle gives a selling price and asks for the loss using that figure. Under those terms, the thirty dollars and seventy dollars are the two amounts that remain after the original bill is accounted for.