The $100 Store Theft Puzzle: How Much Did the Shopkeeper Actually Lose?

An ordinary afternoon at a neighborhood store becomes the setting for a deceptively simple arithmetic puzzle.

Someone quietly takes a $100 bill from the cash register. The shopkeeper does not notice and continues serving customers.

Later, the same person returns and selects merchandise priced at $70. At the counter, they pay with the very same $100 bill they stole.

The shopkeeper accepts the bill, puts it back in the register, and hands over $30 in change.

Then the person leaves with the merchandise and the cash.

How much has the shopkeeper lost?

A) $100
B) $130
C) $170
D) $200

Before reading the explanation, choose an answer.

The numbers are straightforward. The challenge is keeping track of what happens to the stolen bill without counting the same loss twice.

The Correct Answer Is $100

Under the puzzle’s stated values, the shopkeeper loses $100 in total.

That consists of:

• $70 in merchandise
• $30 in cash

Together:

$70 + $30 = $100

The original $100 bill returns to the register during the purchase. Therefore, it should not be counted as an additional missing $100 at the end.

This distinction explains most of the disagreement.

The shopkeeper does not finish with $100 missing from the register plus another $100 missing in merchandise and change.

Instead, the final shortage is $30 in cash and $70 in goods, using the merchandise value given by the puzzle.

Follow the Original Bill

Start by tracking only the $100 bill.

At the beginning, it belongs to the shopkeeper and sits in the cash register.

The person steals it, so the register temporarily contains $100 less than before.

However, the same bill later comes back as payment.

Once the shopkeeper puts it into the register, that particular bill is no longer missing.

This does not make the whole situation harmless. The person receives merchandise and change before leaving.

But it does mean that the original theft cannot be added again as though the bill remained outside the store.

Following that one object through the story prevents the most common double count.

Separate the Story Into Three Events

The puzzle becomes easier when it is divided into distinct events.

First, the theft:
The person removes $100 from the register.

Second, the return of the bill:
The person hands that same $100 back to the shopkeeper.

Third, the exchange at checkout:
The shopkeeper gives away $70 in merchandise and $30 in change.

The first two cash movements cancel each other:

−$100 + $100 = $0

Then the store gives out the merchandise and change:

−$70 − $30 = −$100

This is the complete result. Every part of the story has been included once, and no missing value has been counted twice.

Look at the Cash Register Separately

One source of confusion is treating the total loss as though it must all be missing cash.

In this puzzle, it is not.

The cash movements are:

$100 taken out

$100 returned

$30 given as change

Therefore:

−$100 + $100 − $30 = −$30

At the end, the register contains $30 less cash than it did before the theft.

The remaining part of the total loss is the merchandise.

This is why saying “the shopkeeper lost $100 from the register” would be inaccurate as a description of the final position.

The total is $100, but it is divided between cash and goods.

Now Account for the Merchandise

The person leaves with items priced at $70.

Unlike the original bill, those items do not come back.

Therefore, the merchandise remains part of what the store has lost.

Using the values supplied in the puzzle:

Merchandise loss: $70

Final cash shortage: $30

Combined loss: $100

This method treats the register and the inventory as two separate parts of the same situation.

It is often easier than trying to keep everything in one running mental total.

First determine the final cash difference. Then add the value of the goods that left without a genuine payment from the person’s own funds.

A Complete Transaction Table

The following table shows each event and its effect:

Event	Change in store cash	Change in merchandise value
The person steals the bill	−$100	$0
The same bill returns as payment	+$100	$0
The shopkeeper gives change	−$30	$0
The person takes the goods	$0	−$70
Final difference	−$30	−$70

Add the two final differences:

−$30 + −$70 = −$100

The table also explains why the initial theft does not disappear from the reasoning.

It is included, but so is the return of the same money.

Leaving out either event produces an incomplete account.

Why $200 Is the Wrong Answer

The answer $200 usually comes from adding these amounts:

$100 stolen

$70 in merchandise

$30 in change

That gives:

$100 + $70 + $30 = $200

However, the calculation leaves out the moment when the original $100 returns.

It counts the initial bill as permanently missing while also counting everything received in exchange for it.

To correct that calculation, include the returned money:

$100 + $70 + $30 − $100 = $100

The issue is not difficult addition.

It is an incomplete description of the events. A correct total needs to include money moving back into the store as well as value moving out.

Why $170 Is Also Incorrect

Someone answering $170 may add the original theft to the merchandise:

$100 + $70 = $170

This remembers that the person took goods but overlooks two other parts of the story.

The $100 bill returned to the register, and the shopkeeper handed over $30 in change.

When both movements are included, the result changes:

$100 stolen − $100 returned + $70 in goods + $30 in change = $100

Trying to solve the puzzle by remembering only the largest amounts can make it feel more confusing.

Instead, write every movement down. Each has a place, even when some eventually cancel.

Why $130 Does Not Work

The answer $130 often comes from combining:

$100 stolen + $30 in change

That calculation focuses on the cash taken at two different moments.

However, it does not account for the $100 coming back, and it also leaves out the merchandise.

The final position is clearer:

The register is short by $30, while the store no longer has goods valued at $70.

Therefore:

$30 + $70 = $100

This demonstrates a useful habit for transaction puzzles: ask what is missing at the end.

A list of amounts that moved during the story is not necessarily the same as the final loss.

Check What the Person Walks Away With

Another simple approach is to look at the person’s final position.

They leave with:

$70 in merchandise

$30 in cash

They do not also keep the original $100 bill, because it was handed back at checkout.

Their final gain is therefore:

$70 + $30 = $100

In the simplified situation described, that gain corresponds to the store’s loss.

This provides a useful cross-check on the register method.

Both approaches lead to the same answer, but each highlights something different: one follows the store’s remaining resources, while the other follows what the person ultimately carries away.

Use an Example Starting Balance

If the movements still feel abstract, imagine the register initially contains $500.

After the theft:

$500 − $100 = $400

When the stolen bill returns as payment:

$400 + $100 = $500

After the shopkeeper gives $30 in change:

$500 − $30 = $470

The final cash shortage is therefore $30.

Now include the $70 in merchandise that has left the store:

$30 + $70 = $100

The starting balance of $500 is only an illustration. A different starting amount would not change the result.

It simply makes the return of the original bill easier to see.

Why the Checkout Does Not Create New Money

At first, the purchase may look like a normal sale.

The shopkeeper receives a $100 bill and gives the customer merchandise plus change.

However, the bill originally came from the shopkeeper’s own register.

The person has not introduced $100 of their own money into the store.

Instead, they have used the store’s money to obtain goods and smaller cash.

That is why the bill’s return does not mean the shopkeeper has gained $100 overall.

It restores the earlier cash removal, then the merchandise and change leave.

The sequence matters because each event changes how the next event should be understood.

What If the Merchandise Had a Different Price?

Changing the purchase amount can help check the logic.

Suppose the person uses the stolen $100 bill to obtain $40 in goods and $60 in change.

The final gain is:

$40 + $60 = $100

Alternatively, imagine $90 in goods and $10 in change:

$90 + $10 = $100

Under the same simplified conditions, the division between merchandise and cash changes, but the combined value remains $100.

This comparison works because the person returns the full stolen bill and receives its value in goods and change.

It does not require introducing another theft or a separate payment.

A Note About the Meaning of “Loss”

For this brain teaser, the merchandise is counted at the stated $70 value.

That is the convention behind the answer $100.

A real business analysis could distinguish between an item’s selling price and its cost to the business. The puzzle does not provide that cost information, so it cannot support a separate accounting calculation.

Keeping the assumption visible avoids mixing two different questions.

The riddle asks readers to track the stated values through a simple story. It does not provide a complete financial record of a shop.

Using the values given, the result remains $70 in goods plus $30 in cash.

How to Explain It to Someone Who Disagrees

Begin with a question:

Where is the original $100 bill at the end?

The answer is that it is back in the register.

Then ask:

What did the person take away?

The answer is $70 in goods and $30 in change.

Those two questions often make the situation clearer than repeating the final number.

If more explanation is needed, use the starting-balance example or the transaction table.

Focus on the movements rather than on who answered first.

A useful discussion makes the reasoning visible. Confidence alone does not show whether the returned payment has been included correctly.

The Final Answer: A) $100

The original $100 bill is stolen and then returned.

Afterward, the shopkeeper gives the person:

• $70 in merchandise
• $30 in change

The final cash shortage is $30, and the goods are no longer in the store.

Therefore:

$70 + $30 = $100

The correct choice is A) $100.

If you initially chose $130, $170, or $200, check whether you counted the original bill as permanently missing or left out another part of the exchange.

🧠 What was your first answer? Share the method you used in the comments—and see whether your friends can explain their reasoning too!