Some riddles are challenging because they involve complicated mathematics. Others are difficult for a completely different reason: they make you look at the same amount of money more than once.
This classic shopkeeper puzzle is a great example.
The arithmetic is easy. The real challenge is keeping track of what happens to the money at each stage without accidentally counting the same $100 twice.
So, before looking at the solution, take a moment and see if you can work it out yourself.
The Riddle
A man walks into a shop and steals a $100 bill.
A short time later, he returns to the same shop and uses that exact $100 bill to buy $70 worth of merchandise.
The shopkeeper accepts the bill and gives the man $30 in change.
The Question
How much money does the shopkeeper actually lose?
Is the answer $70?
$100?
$130?
Or even $200?
At first glance, there seem to be several possible answers. That's what makes this puzzle so deceptive.
Let's follow the money carefully.
Step 1: The Man Steals $100
The first event is simple.
The man takes a $100 bill from the shop without paying for it.
At that exact moment, the shopkeeper is missing:
$100 in cash.
The thief now has the $100, while the shopkeeper has suffered a $100 loss.
But the story doesn't end there.
The same stolen bill is about to come back into the shop.
Step 2: The Thief Uses the Stolen Money
The man returns and decides to spend the stolen $100 at the very same store.
He selects $70 worth of merchandise and hands the shopkeeper the $100 bill.
The shopkeeper doesn't know that the money was stolen, so he accepts it as payment.
Now something interesting has happened.
The original $100 bill that was stolen from the shop has returned to the shopkeeper.
That might make you think the shopkeeper has recovered the entire $100 loss.
But that's not the case.
Why?
Because the shopkeeper still has to give the customer change and hand over the merchandise.
Step 3: The Shopkeeper Gives $30 in Change
The merchandise costs $70, but the customer paid with $100.
So the shopkeeper calculates:
$100 − $70 = $30
The customer receives $30 in cash as change.
He also leaves the store with $70 worth of merchandise.
At this point, the thief has walked away with:
- $70 worth of goods
- $30 in cash
Together, those are worth:
$70 + $30 = $100
And that's the key to the entire puzzle.
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