Some riddles are difficult because the math is complicated. Others are tricky because they make us look at the same money from different angles.
This classic shopkeeper riddle is a perfect example. The numbers are simple, but the way the money moves can make the answer surprisingly confusing.
Here’s the puzzle:
A man walks into a shop and steals a $100 bill. He then uses that same $100 bill to purchase $70 worth of merchandise. The shopkeeper accepts the bill and gives him $30 in change.
How much does the shopkeeper actually lose?
At first, the answer seems obvious. But once you start following the $100 bill through each step, it’s easy to second-guess yourself.
Let’s slow it down and solve it logically.
Step 1: The Thief Steals $100
The first part is straightforward.
The man takes a $100 bill from the shop without paying for it.
At this point, the shopkeeper is down:
$100 in cash.
So the shop has already suffered a $100 loss.
But the story doesn’t end there.
Step 2: The Thief Comes Back to Buy Something
The man takes that stolen $100 and uses it to purchase $70 worth of merchandise from the same shop.
This is where the puzzle starts playing tricks with your thinking.
The shopkeeper receives a $100 bill and, not realizing that it was stolen, treats it like a legitimate payment.
But remember: it’s the exact same $100 bill that originally belonged to the shop.
The shopkeeper hasn’t actually recovered the original loss in economic terms. The thief has simply brought the stolen cash back into the store as part of the transaction.
Step 3: The Shopkeeper Gives $30 in Change
Because the merchandise costs $70 and the thief paid with $100, the shopkeeper gives him:
$100 − $70 = $30
in change.
Now look at what the thief leaves with.
He has:
$70 worth of merchandise
$30 in cash
Add those together:
$70 + $30 = $100
That’s the key to the riddle.
So, What’s the Total Loss?
The shopkeeper ultimately loses $100.
The loss consists of:
$70 worth of merchandise + $30 cash = $100
The original $100 bill simply changed hands during the transaction. Counting that same $100 again as an additional loss would mean counting the same money twice.
The Cash Flow in Simple Terms
Here’s another way to look at it:
Initial theft:
Shop loses $100 cash.
Purchase:
The stolen $100 returns to the cash register.
Change:
Shop gives the thief $30.
Merchandise:
Shop gives the thief $70 worth of goods.
Final loss:
$30 cash + $70 merchandise = $100.
Why Do People Get Different Answers?
The wording makes it tempting to add every number mentioned in the story.
Someone might reason:
$100 stolen + $70 merchandise + $30 change = $200
But that doesn’t work because the $70 and $30 together represent the $100 value that the thief ultimately walks away with. The original stolen bill isn’t an additional $100 loss on top of those items.
Another common thought is that the shop loses $130 because it loses the original $100 and then gives away $30.
Again, that double-counts the same transaction.
The cleanest method is to compare what the shop had before the theft with what it has after everything is finished.
The Easiest Way to Solve It
Imagine the shopkeeper starts with the $100 bill.
The thief takes it.
Then, during the purchase, that same bill comes back to the shop.
After the transaction, the thief leaves with $70 in merchandise and $30 in cash.
So the shopkeeper is ultimately missing:
$100 total.
The fact that the $100 bill temporarily returns to the cash register doesn’t erase the original theft. The thief simply converts the stolen cash into merchandise and change.
Final Answer: $100
The shopkeeper loses $100 altogether:
$70 in merchandise
$30 in cash
The $100 bill used for the purchase was the same money stolen at the beginning, so it should not be counted as a second $100 loss.
The Riddle’s Real Trick
This isn’t really a test of difficult arithmetic.
It’s a test of whether you can track the value of an object through several transactions without counting it twice.
Once you stop following the physical $100 bill and instead look at what the shopkeeper is missing at the end, the answer becomes much clearer.
$70 worth of goods + $30 change = $100 lost.
Sometimes the hardest part of a simple math riddle isn’t doing the calculation—it’s figuring out which numbers actually belong in the calculation.
