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
