The Store Thief "Riddle"

This was on Facebook and the fact that two thirds of all people get it wrong really has me wondering what universe I’m living in.

A thief steals a $100 bill from a cash register. He then uses the $100 bill to buy a $70 item, and leaves with the item and $30 in change. How much did the store lose?

The number of people giving the wrong answer makes me wanna barf. (And, no, it does not matter what the cost of item to the store was.)

I say


$100. Doesn’t matter if it’s cash or merch it he’s still walking out with a $100

You’re right of course. It’s really just cash, though, but that isn’t the important part.

That others have a different perspective on the question really shouldn’t cause you to have such a visceral reaction.

The problem is that the question is worded ambiguously(which is kinda the entire point of it being a “riddle” or really a trick question). If the question is how much was stolen from the store, then the answer is $100. But that’s not the question, the question is how much did the store lose.

We are given the information that the two interactions that this store has ever had is a theft of $100, and a purchase of $70. If you are asking how much money did the store lose on those two interactions, then the answer is $100 minus the profits of the sale.

Let’s say that I stole $100 from the store. Then you, completely unrelated to me, come in and buy something for $70, giving them a completely different $100 bill, and get $30 in change. What is the store’s loss over those two interactions? If we are the only two people that come into the store that day, what is the store’s loss for that day?

The way that the question is worded only works to give the amount stolen being the amount lost if the store doesn’t make any money off of selling items.

It is simply a matter of people taking the question at face value, rather than reinterpreting it the way that you have, that causes them to get what you consider to be the “wrong” answer. It doesn’t ask how much the store lost due to theft, it asks what its loss over the interactions we are given information for is.

If it will settle your stomach at all, reframe the question honestly, and ask how much was stolen, and I’m sure you will see far fewer come to an answer that you find objectionable.

The $70 purchase represents a double loss to the store. Sure, on paper, and in a very narrow accounting sense, the store has recouped $70 of the stolen $100 – BUT only on paper. In actuality, the store has suffered two separate losses; the $100 in cash, and the $70 in lost sales.

If the OP has trouble understanding this, try this thought experiment–
Divide the assets of the store into two categories:

  1. Cash assets (loss of $100)
  2. Inventory assets (loss of $70)

The thief stole from the store’s inventory just as surely as if he had not pretended to buy it. The store merely, and incorrectly, thinks that he bought it.

While an interpretation of the question can get to the $100 loss, if we are adding “due to theft” to the question, even though that is not in it, your double loss doesn’t work at all.

The thief bought the item, that was a real sale. If there was no theft, and all that happened was that someone bought a $70 item, then it would be ludicrous to say that it was lost sales. That it was bought with the stolen money doesn’t mean that it wasn’t a real sale, the store really got that $70, the same as if it were bought by someone entirely different.

Same thought experiment for you. I steal $100 from the store and go spend it elsewhere on drugs and gambling. Then you go into the store and buy something for $70. Does that represent a double loss to the store? Does the store incorrectly merely think that you bought it?

  1. It’s actually the same as taking the $100 and returning the $100, so zero loss.
  2. Then taking the 70$ item and $30 in cash, for a loss of $100 (ignoring costs and margins and bears, oh my).

So out $100.

The store is correct. He bought it. The store is out $100 in cash.

Look, the morality of this seems to fool people or something, though I don’t get why. So imagine this happens:

The thief steals the $100… and then he leaves. Another person, using a different $100 bill, buys a $70 item.

What did the store lose? $100 in cash. But that is mathematically exactly the same. All $100 bills are the same value, it doesn’t matter which one was used to buy the item or who spent it.

At the end of the day the register will be $100 short. Inventory will not be short at all.

I am not an accountant but isn’t the overall liability (as in unsold stock) of the store reduced by this? I mean they are still down but on the balance sheet less than if he’d just walked off with the $100.

Even without accounting shenanigans it seems the actual value of that guitar to the store is $70 multiplied by the chance of someone else actually buying it.

Let’s say that the store had $2000 in sales that day at a 10% profit. At the end of the day, inventory is taken and the register is counted.

Maybe the thief bought something, maybe they didn’t, it doesn’t matter here.

I see that I made $200 in profit off of sales, but lost $100 due to theft. My business partner asks me how much we made today. Do I say $100, or do I say that we lost $100?

I would say that we made $200 in profit on sales, but lost $100 to theft, so we made $100 that day. There is no reason why I would just say that I lost $100.

If he asks how much was stolen, or how much we lost due to theft, then I would answer $100.

That’s not the question, though. Yes, the store made money at other times or else it would not exist. The question is about what happens in the example.

Right, and the example covers two interactions, and asks how much the store lost between the two of them. I’m just pointing out that taking the question at face value means subtracting the profit of the sale from the loss from the theft.

I was expanding on the example into a real world situation to show how bad this question is at getting the answer that you feel is the “right” one.

Only by adding the words, “due to theft”, or rephrasing as “how much was stolen” does the question only look at that half of the interactions.

Like I said, the question is intentionally ambiguous in order to create exactly this sort of dissonance. It is contrived for this purpose. If you want a better answer, ask a better question.

Nope. You are making @RickJay wanna barf.

If you look at it that way, then the store’s loss is what they paid for the item plus the $30.

Shrinkage is calculated based on cost, not on price.

Sure, which is why I was very careful to say if you ignore costs, margins, etc.

I completely agree with you that it’s a poorly worded riddle, but it’s not like it’s the first time we’ve seen something like this. You basically have to ignore those things and assume that all goods cost zero dollars, so a $70 item is worth $70 dollars in value. The way that the originator wants you to look at the problem, and I didn’t find particularly confusing, is the following:

Before any of the thievery takes place:
You have $1000 in cash
You have $1000 worth of inventory (again, ignore COGS).

At the end of all the outlined transactions:
You have $970 in cash
You have $930 in inventory

You started with a value of $2000, now you have a value of $1900, so you’re out $100. If the riddle had wanted actual inventory management policies to be taken into account (and again, I agree with you that it’s a poorly laid out riddle), we would have been given a COGS value for the item.

I think it would have to be the other way around, in where all goods cost their retail value. Otherwise, there is profit to be had in selling the item, which offsets the loss from the theft.

If the riddle wants you to give an exact dollar figure, sure. But $100 minus the profit from the sale is as good an answer as an exact dollar figure.

If the riddle had wanted to know how much was stolen, or how much was lost due to theft, then it would have used those words. Instead, it described two interactions, and asked how much was lost between those two interactions.

And I don’t think that it is “poorly laid out”, I think that it is intentionally made ambiguous specifically so that different people will come to different answers based on how they interpret what is left out of it.

I feel like you’re trying to argue past me for some reason, so let me ask two yes/no questions.

  1. Do you think that I answered the riddle with the answer that the author would agree was the correct one?
  2. Can you answer the riddle correctly, with a final specific dollar amount, in the way you understand it should be without being given the cost of the $70 retail item?

If your answers are Yes and No respectively, then I see no disagreement.

I agree with k9bfriender, unless you are sure to sell all your stock due to product craze or something.

Store open: Assets = $500 cash, $500 worth of goods
Theft of $100: assets = $400 cash, $500 worth of goods
Purchase by thief: assets = $470 cash, $440 worth of goods ($10 profit)
Store close: assets = $470 cash, $440 worth of goods

From open to close how much did you lose? 500+500=1000, 470+440=910. That sale probably wasn’t going to be made anyways. So it would appear we lost $90.

But let’s say the thief purchased the last item in stock during a consumer craze. It was going to be sold anyways. In which case, if the thief had not stolen or purchased anything we could have had $1070 at the end of the day. The loss would be $160.


  1. I think the author intentionally created a trick question, knowing that it would be ambiguous and would have no “right” answer. If the author actually meant for it to be unambiguously answered as to how much was stolen, then it was actually just a very poorly phrased question, and the author’s intent is irrelevant as they are apparently too stupid to ask a question properly.

  2. No, but if the author wants a specific dollar figure, then they did not give enough information to give one, nor did they actually ask for one. That’s not the fault of the person answering the question, that’s a lack of information given by the questioner. No different than if I ask you what 100-70+70-30+30-x is. The answer is 100-x, and it doesn’t invalidate the answer that you don’t know what x is.

I think our disagreement is the motive of the author. You seem to think that he asked a straightforward question with a definite answer. I think that he intentionally asked an ambiguous question that he knew would have an ambiguous answer.

ETA: I’m gud at maf.

  1. You didn’t actually answer my first question with a yes or no, but I’m going to infer that you agree with me.
  2. Absolutely, but the lack of information in this case gave me confidence that my understanding of their intent was accurate.

I think you’ll be hard pressed to find where I said it was a straightforward question. I understood the intent, primarily because no cost was given and I’ve seen such things a million time before.