At first glance, this looks like one of those math problems that should take only a few seconds to solve.
A man steals $100 from a shop.
Then he comes back and uses that same $100 to buy $70 worth of merchandise.
The shopkeeper gives him $30 in change.
Simple, right?
But ask someone how much the shopkeeper actually lost, and you may hear several different answers.
Some people say $100.
Others say $130.
And a few will confidently argue that the answer is $200.
So which one is correct?
The trick isn't complicated mathematics.
It's about following the value instead of accidentally counting the same $100 twice.
Let's walk through the entire transaction.
The Riddle
Here is the puzzle in its simplest form:
A man enters a shop and steals a $100 bill.
He later returns and uses that same $100 bill to buy $70 worth of merchandise.
The shopkeeper accepts the bill and gives him $30 in change.How much has the shopkeeper actually lost?
Take a moment before reading further.
The answer may seem obvious, but the wording is designed to make you count the money in more than one way.
First: The Man Steals $100
At the beginning, the shopkeeper has a $100 bill.
The thief takes it.
So, immediately after the theft, the shopkeeper is missing:
$100 in cash.
That's straightforward.
But now the thief returns to the same shop.
This is where the puzzle gets interesting.
Second: He Uses the Stolen Money
The thief takes the stolen $100 bill and uses it to purchase merchandise worth $70.
The shopkeeper doesn't know the bill was stolen.
From the shopkeeper's perspective, a customer has simply handed over $100 to pay for a $70 purchase.
So the shopkeeper puts the $100 bill back into the cash register.
At this moment, it might feel as though the shopkeeper has recovered the stolen money.
But that's not the end of the transaction.
The shopkeeper now owes the customer change.
Third: The Shopkeeper Gives Back $30
The merchandise costs $70.
The customer paid with $100.
Therefore:
$100 − $70 = $30
The shopkeeper gives the thief $30.
Now let's look at everything the thief walks out of the store with.
He has:
$70 worth of merchandise
plus
$30 in cash.
Together, that's:
$70 + $30 = $100.
And that's the key.
The Final Loss Is $100
Once all the transactions are complete, the shopkeeper has lost:
$70 worth of merchandise
$30 in cash
Total:
$100.
The original $100 bill has returned to the shop.
That's why you cannot count that bill as another $100 loss after the transaction.
The thief has effectively transformed the stolen $100 into $70 worth of goods plus $30 cash.
Why Some People Answer $200
This is where the riddle catches people.
A person might look at all the numbers and think:
$100 stolen + $70 merchandise + $30 change = $200
It seems logical at first.
But there's a problem.
The $100 stolen at the beginning is the same $100 bill that comes back into the shop.
You're counting it twice.
Think of it as one object moving around.
The thief takes the bill.
Then he gives the bill back to the shopkeeper.
The shopkeeper then gives him merchandise and $30.
The original bill doesn't disappear.
It simply returns to the cash register.
Why $130 Is Also Incorrect
Another common answer is:
$100 + $30 = $130.
The reasoning might be:
“The shopkeeper lost $100 when the thief stole the bill, then lost another $30 by giving change.”
But that still ignores the fact that the stolen $100 comes back.
Once the thief uses the bill to make the purchase, the shopkeeper has that $100 again.
What remains missing is the value of the merchandise and the $30 change.
So:
$70 + $30 = $100.
Think About What the Shopkeeper Has at the End
The easiest way to solve the puzzle is to stop focusing on the movement of the $100 bill.
Instead, compare the shop's situation before and after everything happens.
Before the theft
The shopkeeper has:
$100 cash + $70 worth of merchandise
For simplicity, we're only tracking the items involved in the riddle.
After the transaction
The shopkeeper gets the stolen $100 bill back.
But gives the thief:
$70 in merchandise + $30 cash.
Therefore, compared with where the shop started, the shopkeeper is missing:
$70 merchandise + $30 cash = $100.
That's the cleanest way to see it.
The $100 Bill Is the Distraction
The physical bill is what makes this riddle confusing.
Your brain naturally wants to follow it.
You see:
$100 → stolen → returned → change given
And because the same bill appears several times in the story, it can feel like several different losses are happening.
But there is only one $100 bill.
It begins in the shop.
It leaves.
It comes back.
Then the thief leaves with $100 worth of value in another form.
That's all.
Imagine the Thief Had Used a Different $100 Bill
Here's another way to understand the trick.
Imagine the thief somehow had another legitimate $100 bill and used that to buy the merchandise.
The shopkeeper would receive $100 and give back $30, while handing over $70 worth of goods.
The net result of that transaction would be:
$100 received − $30 change − $70 merchandise = $0.
There would be no loss from the purchase itself.
The shopkeeper would simply have exchanged $100 for $70 of merchandise plus $30.
But in the actual riddle, the $100 used for the purchase was already stolen from the shop.
That means the thief has gained $100 of value while the shopkeeper ultimately loses $100 of value.
Another Simple Example
Suppose instead the stolen bill were $50.
The thief steals $50.
He returns and buys $35 worth of goods.
The shopkeeper gives him $15 change.
What does the thief leave with?
$35 + $15 = $50.
And what does the shopkeeper lose?
$50.
The same principle works regardless of the numbers.
The thief converts the stolen cash into merchandise and change.
What If the Merchandise Is Worth $70 at Retail Price?
There is one subtle point worth mentioning.
The riddle normally treats the merchandise as having a value of $70.
In real business accounting, the shopkeeper's actual economic loss could depend on the goods' cost to the shop, not their retail selling price.
For example, if an item sells for $70 but cost the store $40 to purchase, the accounting loss associated with giving it away might be different from $70.
But that's not how the classic riddle is framed.
The puzzle asks about the stated value of what the thief receives.
Under that assumption, the answer is:
$100.
A Timeline Makes It Even Easier
Let's put the entire story into four simple stages.
Stage 1: Theft
The thief takes:
$100 cash
Shopkeeper's loss so far:
$100
Stage 2: Purchase
The thief gives the same:
$100
back to the shopkeeper.
The bill returns to the shop.
Stage 3: Change
The shopkeeper gives:
$30 cash
to the thief.
Stage 4: Merchandise
The shopkeeper gives:
$70 worth of goods
to the thief.
Now calculate the final value that has left the shop:
$30 + $70 = $100.
That's the answer.
Why These Riddles Are So Effective
The arithmetic is almost ridiculously easy.
That's what makes the puzzle work.
There are no complicated formulas.
No multiplication.
No fractions.
No difficult percentages.
Instead, the challenge is tracking the same object through several stages.
Our brains are naturally tempted to add every number we see.
But not every number represents a separate loss.
Some numbers describe the same money at different moments.
That's a useful lesson that goes beyond riddles.
The Most Important Rule: Don't Count the Same Money Twice
Whenever you encounter a puzzle involving money moving between people, ask yourself:
Is this a new amount of money, or is it the same money appearing again?
In this case, the $100 appears multiple times.
But it is still just one $100 bill.
Counting it once as a theft and again as a separate loss would create an artificial $200 total.
The correct approach is to calculate the final difference.
So Who Gets What?
At the end of the story:
The thief receives:
$70 worth of merchandise
$30 in cash
Total value:
$100
The shopkeeper receives:
The stolen $100 bill back
But the shopkeeper gives away:
$70 in merchandise
$30 in change
So the shopkeeper's net loss is:
$100.
The Answer in One Sentence
If you want the shortest possible solution:
The shopkeeper loses $100 because the thief ultimately leaves with $70 worth of merchandise and $30 in cash, while the original $100 bill returns to the shop.
That's it.
The Real Trick Behind the Puzzle
The riddle isn't really asking whether you can subtract $70 from $100.
Almost anyone can do that.
It's testing whether you can distinguish between:
cash flow and final loss.
The $100 bill moves from the shop to the thief and then back to the shop.
That movement doesn't create a second $100 loss.
The actual loss is whatever the thief keeps after the transaction.
And what does he keep?
$70 + $30 = $100.
Final Answer: $100
So if you chose $100, you got it.
The shopkeeper's final loss is:
$70 in merchandise + $30 in cash = $100.
The original $100 bill was stolen, but then returned to the shop when the thief used it to make his purchase.
That's why answers such as $130 or $200 result from counting the same money more than once.
The next time you see a riddle involving money changing hands, don't rush to add every number you see.
Follow the money.
Ask what was there at the beginning.
Then ask what remains at the end.
Sometimes the trick isn't in the math at all.
It's in knowing which numbers you're actually supposed to count.
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