So How Much Did the Shopkeeper Lose?
The answer is:
$100
The shopkeeper ultimately loses $70 worth of merchandise plus $30 in cash.
$70 + $30 = $100
The original $100 bill isn't an additional $100 loss because it is the same bill that was stolen at the beginning and later used to make the purchase.
Counting it again would mean counting the same value twice.
Let's Look at the Entire Transaction
Sometimes the easiest way to understand this puzzle is to ignore the confusing movement of the physical bill and compare what the shop had before and after the entire incident.
Before the theft
The shopkeeper has the $100 bill and $70 worth of merchandise.
After everything is finished
The thief has:
- The $70 worth of merchandise
- The $30 in cash
The shopkeeper has received the stolen $100 bill back, but has given away goods worth $70 and cash worth $30.
Therefore:
$70 + $30 = $100
That's the shopkeeper's total loss.
Why Isn't the Answer $200?
This is one of the most common mistakes people make with this riddle.
Someone might add all the numbers together:
$100 stolen + $70 merchandise + $30 change = $200
It looks reasonable at first.
But there's a problem.
The $70 merchandise and $30 change already add up to $100. That $100 represents the value that the thief ultimately takes away from the shop.
The original stolen $100 bill is the same money that comes back during the purchase.
So adding another $100 would count the same value twice.
Why Isn't the Answer $130?
Another common answer is $130.
The reasoning usually goes something like this:
- The shopkeeper initially loses $100.
- The thief later receives $30 in change.
- Therefore, the loss is $130.
But this also counts part of the transaction incorrectly.
The stolen $100 returns to the shop during the purchase. In exchange, the shopkeeper gives the thief $70 worth of merchandise and $30 in cash.
So the final loss isn't the original $100 plus another $30.
Instead, the stolen $100 has effectively been transformed into:
$70 in merchandise + $30 in change.
That's still exactly $100.
A Simple Cash-Flow Breakdown
Here's the puzzle in its simplest form.
1. The thief steals $100
Shopkeeper: −$100
2. The thief returns and spends the same $100
The $100 bill comes back to the shop.
Shopkeeper: +$100
3. The shopkeeper gives $30 change
Shopkeeper: −$30
4. The shopkeeper gives away $70 worth of merchandise
Shopkeeper: −$70
Now calculate the final result:
−$100 + $100 − $30 − $70 = −$100
So the total loss is:
$100
The Trick Is in Following the Value, Not Just the Bill
The puzzle becomes confusing when you focus too much on the physical $100 bill.
The bill itself moves around:
Shop → Thief → Shop
But the shopkeeper's final loss comes from what the thief walks away with.
The thief ultimately leaves the store with:
$30 cash + $70 merchandise = $100
That's why the final answer is $100.
The $100 bill returning to the register doesn't create an extra $100 of value. It simply allows the transaction to take place.
Try Solving It Without Looking at the Numbers
There's another useful way to think about the puzzle.
Imagine the shopkeeper could somehow freeze the situation at the very end.
What has the thief taken from the shop?
He has:
- $70 worth of products
- $30 in cash
That's it.
The original $100 bill is no longer with him. It has returned to the shop.
So the shopkeeper is missing exactly:
$100 in total value.
This perspective makes the answer much easier to see.
The Final Answer
The shopkeeper loses $100.
The breakdown is:
$70 worth of merchandise
+ $30 in cash
= $100 total loss
The $100 bill used in the purchase is the exact same $100 bill that was stolen earlier, so it should not be counted as an additional loss.
Why This Riddle Is So Tricky
This puzzle isn't really testing your ability to perform difficult calculations.
It's testing whether you can follow money through multiple transactions without double-counting it.
The numbers are deliberately chosen to make the situation feel more complicated than it actually is.
Once you separate the transactions and look at what the thief actually takes away, the solution becomes straightforward.
The key equation is:
$70 merchandise + $30 change = $100
So, despite all the movement of money, the shopkeeper's final loss is:
$100
Sometimes the hardest part of a simple math puzzle isn't doing the arithmetic.
It's knowing which numbers should be counted—and which ones are simply different appearances of the same value.
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