HOW SMART ARE YOU? The Stolen Bill Riddle (Viral Math Problem) – The Correct Answer Explained
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HOW SMART ARE YOU? The Stolen Bill Riddle (Viral Math Problem) – The Correct Answer Explained

August 24, 2019

Hey this is Presh Talwalkar. I received this problem by email because it’s going viral on Facebook with thousands of people arguing about the correct answer. How smart are you? A guy walks into a store and steals a hundred-dollar bill from the register without the owner’s knowledge. He then buys seventy dollars worth of good using the hundred-dollar bill and the owner gives thirty dollars in change. How much money did the owner lose? Was it $30, $70, $100, $130, $170, or $200? Can you figure it out? Give this problem a try and when you’re ready keep watching the video for the correct answer. In some math problems, and in this story, it helps to break the problem down into different parts so at first we’ll only consider the first part of the story. A guy walks into a store and steals a hundred-dollar bill from the register without the owner’s knowledge. At this point how much does the owner lose? Everyone agrees the owner loses a hundred dollars. The owner is at minus 100 from the initial part of the story. So now let’s separately consider just the second part of the story. Imagine someone buys seventy dollars worth of goods using a hundred-dollar bill and the owner gives thirty dollars in change. How much would you say the owner has lost in just this part of the story? Well if someone buys seventy dollars worth of good using a hundred-dollar bill you would expect the owner to give thirty dollars in change. In fact the owner is overseeing this transaction. So the owner here is not losing any money. The owner is you could say zero in this transaction. So now we put these two stories together the total loss will be the sum of these two parts of the story so we can add -100 and 0 to get the total loss is $100 the owner is negative one hundred dollars from before the story started the correct answer is the owner lost $100. Now there’s one technicality if you want to really overthink this problem and go into the accounting details. Now when someone buys seventy dollars worth of goods in a store it’s not because the goods are worth seventy dollars to the owner. What happens here is the owner is getting a hundred-dollar bill and gives back thirty dollars in change but the goods have some value V. This is usually going to be less than seventy dollars so you could say the owner’s actually losing the value of the goods but then getting a net seventy dollars because it’s a hundred-dollar bill minus thirty dollars in change but here the owner loses V minus 70 or you could say the owner is 70 minus V in terms of the cash position so if you were to take these two stories now you add up the result the owner ultimately loses thirty dollars plus the value V of the goods so if we assume the value V is seventy dollars which you say seventy dollars worth of goods then you would say the owner lost a hundred dollars. So you can still arrive at the same answer of a hundred dollars but this is a little more accurate in terms of pure accounting. So why are so many people getting this problem wrong? Well one of the common answers is there is a two-hundred-dollar loss to the owner. Many people think this is because in the first part of the story the owner loses a hundred dollars that’s stolen and then in the second part of the story the owner loses another hundred dollars because the owner is giving up seventy dollars worth of goods and thirty dollars in change. So the mistake here is that it’s not taking into account the owner is also getting a hundred-dollar bill so when you take that other part of the story where you get the hundred-dollar bill that will adjust the total by +100 and when you do that, that means the owner ultimately lost a hundred dollars in total. Another common answer is that the owner had a $130 loss. This is from the stolen hundred-dollar bill and the thirty dollars in change. Well the problem with this answer is it’s not taking into account that the owner also gave up seventy dollars in goods but also got a hundred-dollar bill so when you take into account these transactions the net result would be the owner losing $100 which is negative 100. So to summarize most of the incorrect responses either didn’t add or subtract numbers correctly or they didn’t take into account every transaction. It seems the fact that in the second half of the story that person used the stolen dollar bill somehow people don’t treat that as a genuine hundred-dollar bill. That is a hundred dollars that the owner’s getting back. So when you take into account every single transaction and you treated correctly as either a loss or gain for the owner you end up that the owner lost a hundred dollars. Did you figure it out? Thanks for watching this video please subscribe to my channel i make videos on math and game theory you can catch me on my blog Mind Your Decisions you can follow on facebook google+ and patreon you can catch me on social media @preshtalwalkar if you like this video please check out my books there are links in the description.

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  1. he stole 100, gave back 100 to the owner (owner has no lose yet). Then, the owner loses 70 (worth of good) plus 30 (change), which in total he lose 100

  2. His loss is $30 and $70 worth of goods, but when he balances his books, he's going to find he's got $100 less, not the $30 and the $70 worth of goods. He won't realize that what was actually stolen eventually was the purchase that was made. He has no reason to believe that the stolen $100 is what was used to make this purchase that he does know about.

  3. I think that any answer is correct, cause the interpretation of what the problem it depends on each and one of us. However i believe that the correct answer is $130, because i am considering productos and cash as 1. Being said, the owner begins with -100 and +70 in products (assuming that he does not have more products nor more money in the register, and no profit will be made). So then the transaction begins, -$100+$70(cash of the lady)-$70 (goods)-$30(change).

  4. This "viral math problem" is flawed and the flaw is explained in this video. What the owner loses is $30 plus the value of the goods (what the owner paid for the goods). That value is represented by V in this video. In this video, V is assumed to be $70. Why? I have no idea. V could be anything from 0 – 70. But it is more likely that V < 70. Why because no profitable business sells goods at cost. So because V is unknown, you can't calculate how much the owner lost.

  5. this owner has lost more than 100 but less than 170. the owner has to have paid for the item at some point. so the owner is net lost at -(100 + cost of the item) after you have stolen the 100. just because you gave him back 70 does not account for the fact that the money was the owners to begin with, and they gave you back 30. so you just made off with 30 + the item, leaving the owner with -30, 70 of HIS OWN MONEY, and one less product that was practically given for free, because it was paid for by his own money.

  6. $100 of course.
    Well actually a bit less if you consider that he makes a little profit when selling a $70 object (because he didn't pay that much for it)

  7. It says how much money did the owner lost and that would be 30 dollars. It didn't say how much in total did the owner loses. Common sense

  8. The way I think of it is that the theft and the purchases are independent events, making the theft irrelevant to the purchases. So the loss is just what is lost from the theft: $100.

    However, this got me thinking. Dangerous, I know 😉. Is the theft actually irrelevant to the purchases? Would the thief have made those purchases if he had not had the $100? I realize this goes beyond the scope of the problem. But, from a microeconomics perspective, does the gained business come into it? He's still out the $100, but does the thief's marginal propensity to consume translate into the business owner gaining back some percentage of his loss because of the business he would otherwise not have gotten? I think I know just enough economics to be dangerous.

  9. The owner lost $100.When the guy bought the goods,the owner receives back $70.Therefore the owner loses $100-$70=$30.

  10. This is a dumbed down version of the "value of the lost ticket" problem that economists argued over a few years back. In that problem the fight was over different definitions of the word "value."

  11. This doesn't take into a count that the owner only loses costnprice of the good. Not his price. So if he only paid 5 dollars for the goods but charged and outrageous 70. Then gives 30 in change. He has inly lost 35 dollars.

  12. The narrator of this video is Flat. Out. Wrong. The owner did NOT lose 100 dollars if the 100 dollars is in the til,l DID he? His ACTUAL overall loss was 30 dollars and some goods. But the question doesn't ask what VALUE he lost, it asks how much MONEY he lost. His loss was 30 dollars and some goods. How much MONEY did he lose? Think.

  13. The narrator’s exact mistake is at 3:04 of this video where he says, “you could say the store owner loses the value of the goods but gets the 70 dollars in exchange.” He is erroneously ignoring the fact that if the robber doesn’t steal the 100, there is no sale. This means the inventory is valued at the lesser of cost or market value before the robber comes. Since we don’t know what the owner paid for the goods, we can’t determine the value to be 70 dollars. No robber, no sale, no 70 dollars. Just inventory. But all of that is irrelevant, because from start to finish, the owner’s overall loss is thirty dollars plus some goods. And no matter WHAT those goods are valued at is irrelevant, because goods aren’t money, and puzzle SPECIFICALLY asks how much MONEY the owner lost. A) 30

  14. The truth is money is a social construct and no existing mode of capitalism even vaguely resembles the hypothetical free markets of econ 101, otherwise it'd be impossible for corporations to exploit us in the way they do.

    Hypothetically the owner loses $30. In truth, the owner loses a set of metal discs and some bad smelling cotton

  15. Owner lost 100 dollars and another 70 worth of goods, but then he got 70 dollars back, and technically, since the 100 dollar bill was his… he lost another 30, resulting in minus 130

  16. your explanation is wrong.

    accounting factors in the till loss AND the stock loss.

    the stock loss is calculated at full sale price(opportunity cost)


  18. He missing $130
    He’s was robbed $100
    Got back $70/$100
    Still missing $30 to complete $100 stolen
    Still missing $70 for the actual purchase
    And then he gave away $30 in change (which he was suppose to keep since it was to complete the $100 that was stolen )

    – So in total $70 from merch, $30 from change, and $30 to complete the $100

  19. Overexplaining over and over again.
    Someone steals 100$. The loss is 100$.
    Everything that follows is exchange transactions.

  20. From my Layman's perspective. From where will the owner find $30 change to give, if the thief emptied the cash register by stealing the $100? My guess is that the owner may borrow it from somewhere or someone to facilitate the supposed transaction as he has $0 cash and he is unknowingly; loosing fraudulently, the $70 hat to the thief. If the thief carried out the transaction with $100 and the owner gives the thief the $30 change he borrowed, at this stage his deficit looks like $170 ($100 + the hat) + $(30) borrowed = $-200. The thief leaves with (the hat $70* + $30 change that the owner borrowed) after releasing the $(100) = The deficit reduced to $-100* – $30 (returned to where or whom it was borrowed) = $-70. So at this stage he knows that he was defrauded of his hat and his deficit looks like at least $(130). Because at the end of the day the thief should have nothing. The $30 should not have been borrowed for change. And the owner should be in possession of $100 + the hat worth $70. So the fraudulent actions of the thief triggered the movement of at least $200 at the unfortunate expense of unsuspecting owner.

  21. -$100
    He bough $70 in goods, and gave the store $70. The $30 in change is just because he bouht with the $100 dollar bill.
    In the end, he just switch the $70 in money with $70 in goods.

  22. Some folks read way more into this than is necessary.. and many don't understand retail. Profit is beside the point.

    Whatever a product is marked as is it's intended dollar value.. "product" equals dollars in retail. The thief left the store with $70 in product and $30 in change.. paid for with the $100 bill they stole from the store in the beginning.

    The owner got his $100 bill back, but then lost $100 in product and change.

  23. The technicality is actually irrelevant. The value of the goods v actually doesn't matter because on a normal day the owner is expecting to turn a profit by selling those goods, that are worth v dollars, for 70 dollars.

    The owner loses out on the opportunity of getting that profit that the owner expects to get, which in turn is worth $70. So in fact, the owner still loses $70 dollars.

  24. The store loses $130
    $100( $70 stuff+ $30 still with him)+ $30( the change, the owner thinks the $100 is not from the register)
    100+30= 130

  25. At first, I thought the answer was $130, and after you gave the answer, I wondered why the loss was $100. After thinking a little bit, I realized this situation is (in effect) no different than if the man stole the $100 bill but paid for the $70 worth of goods with his own money. It doesn't matter whether he paid exactly with his own money, or overpaid and received change. Everything was properly paid for, but $100 was stolen. The owner of the store lost $100.

  26. The answer is 30 as the goods are already owned by the store. The store owner is only profiting when he gets that 70 dollars so all he really did was give the guy 30 bucks. The equation would be -100+70=-30. You can say it’s an even transaction but the store in reality already lost the money purchasing the goods wholesale.

  27. This riddle made me lose my mind, I didn't even think it was difficult, I always said it was $100, people getting it wrong made me ill

  28. Moral of the story :If Americans arent smart enough to do math, they probably shouldnt be voting either. 😁

  29. He obviously lost 100. But these 100 have to be somewhere else… As the only information available is about the thieve then he must have them. As he also has 70 worth of goods, he actually has 170 total. Therefore the shop keeper lost 170. But actually 100 value gained by the thief included the 70 of the goods, so the shop keeper lost only 30. There are three different solutions so let's assume the answer is (100 + 170 + 30) / 3 = 100. Qem.

  30. Just reverse the order … a person buys $70 worth goods in a valid transaction.
    He then steals a $100 dollar bill … so the owner loses $100.

  31. 100 dollars was stolen. Anything that happens after that doesn't matter. It won't matter if the same person came back to buy something with a 100 dollar bill or someone else did, the same day, year or whatever… the owner lost 100 dollars.
    The only way he'd get that hundred back is if the thief, or anyone, gave him 100 dollars for nothing.

  32. Actually if you go in even deeper you could say that the shop also lost the cost of the goods that brought in the $100 originally plus if there was change from that sale…

  33. The owner loses $100.

    Profit margins etc are irrelevant. To prove how ridiculous this idea is consider the following two options:

    1. What if the thief uses a different $100 note?
    2. What if the thief didn't buy anything but another customer used a $100 note to buy the item?

  34. Before I watched this video this was my response on Facebook:

    Let’s say you are the owner. The net amount of money that was stolen from you is $30 ($100 – $70). She gave you back the $70 which now removes it from the equation.

    The owner’s loss is $30 cash + the value of the goods taken.

    What is the value of the goods?

    1) The value of the goods in POTENTIAL sales is $70 but that is NOT pure profit. The owner did not buy $70 worth of goods from his supplier for $0.

    2) The COST of those goods to the owner is what the owner paid the supplier. i.e.: $10, $20, $30, etc.


    1) THE ACTUAL LOSS IS $30 cash + WHAT THE OWNER PAID HIS/HER SUPPLIER for those goods that were taken by the lady.

    2) THE POTENTIAL LOSS is $30 cash + the MARKUP OF THE GOODS STOLEN ($70 minus the amount the owner paid his/her supplier for those goods)

  35. The real answer is:
    The $30 is easy. That's how much money the man walks away with but what isn't stated is the cost of the goods he walked away with.

    The cost would include the price the owner paid to buy the goods from the vender, and wage paid to stock and sell the items, and cost to store items until sell.

    There's no way to know that from this problem without the item cost stated.

  36. The answer is B) 70

    There are TWO transactions here we are being asked to consider:

    1) The thief stole 100, so the owner gains -100 (100 loss).

    2) Someone walks in and buys 70 worth of stuff. The owner (assumedly) makes a profit. The owner gains +X (as it’s an unknown for now).

    So total profit for the owner based on the two transactions is equal to X-100

    We can assume for 70 worth of goods that the profit on those goods sold would be likely between 1 and 69 dollars (assuming owner is selling products for profit and the cost of the goods is non-zero).

    Therefor owner’s profit is between 1-100=-99 and 69-100=-31

    So a loss of anywhere between 31 and 99 dollars. The only answer that fits this range is b) 70.

    So the most correct answer is b) 70, is how much total value the owner lost.

  37. I still disagree….

    I go back and forth between these 2 for my final answer….

    V = Value of Item
    O = Original Cost

    Projected Total Loss
    PL= (-(V)) + (-(O)) + (-30)
    or for the simpletons…

    Gross Loss
    GL = (-(O)) + (-30)
    and again

    Either way I disagree with the OP

  38. Funny thing is you cant steal the profit from a business, until it's actually made that profit. $30 + the cost for the goods the store bought wholesale or to replace the goods. There is actual loss and theoretical loss. What the business could have sold the goods for retail. You have to account for the actual cost of the goods, the store bought them foror to replace them if higher. If not lets say a month later the store has a sale everything off 25% or 50% just to make things more easy. Then the goods they stole are worth 52.50 or $35 retail. LOL and no why you use actual cost to find the answer. Easy peas. You cant tell the business loss with out knowing the mark up of the goods.

  39. My problem with this answer is that the owner is getting back his original $100. In other words the thief is using the store's money to buy the goods. So if the manager is unaware of this he's going to think he's only out of $100. However if he knew the whole situation he would say I'm out $200.

  40. Just imagine the crook walks in naked before hand with absolutely nothing with him. What does he leave with? $30 and $70 in goods. Case closed.

  41. Pure math gives you $100

    Pure Accounting gives you $100 loss and loss of goods worth 70 (depends on marginal cost)

  42. As explained in the video, the real most accurate answer is $30+V. The regular answer of $100 includes "potential earnings", though potential earnings are not real losses. In this scenario, the cash register would come up $100 short anyways and inventory would show normal. My favorite part about math and accounting is that YOU ARE EITHER RIGHT OR WRONG. Opinions don't matter.

  43. You are WRONG !!! The answer is 100 but your analysis is wrong because the thief money can not corresponds with a product that you sold in the end of the day
    Also the loss is not 0 beacause you have to be extra cause you gave him product.
    Shame that you give the correct answers to the people.
    Sorry about my English.

  44. My final answer was $170 but i did the math that day and lets say the store has $500. It has $70 of goods around. He is suppose to gain 70 so the store is suppose to have $570 after the goods got payed for. Instead he lost 100. So what happened was $500-100= $400 remaining. No matter who came back they came with 100 and paid for the goods and got 30 dollars change. So that $400 + 70= $470. What he would have gained was $70 dollars because he would have had $570 but instead he has $470 dollars. His loss can he found by subtracting. $570-$470 =$100

  45. in your second solution, the owner dont lose less that 100 because he bought the things cheaper but he is not using them for himself, he is selling them so he lose 70 dollars from selling them (btw i dont know very good english so dont dodge it)

  46. The answer is $30. Why? Because the question specifically asks how much MONEY the owner lost.

    The goods are not money, even though they have a value expressed in dollars, they are still not money.

  47. what you all are missing is the 100 taken from the register was not stolen freely hence the word register receipts are counted at the end of the night right it was registered. so that 100 is missing and 70 in merch and 30 in change that is 200 dollars the drawer will be short 130$ and 70 in merch is gone.

  48. this is via a leftist view, who think everything is free, yet its wrong cause, he stole the 100 from the owner, , u steal 100 from me, then come into my store with the 100 dollars you stole, so it is 100 you stole from me, and now your using the 100 you stole from me to purchase 70 dollars in goods, so the 100 u stole from me means i am out 100 already, now your going to use that to purchase 70 in goods from me, with my stolen 100 dollars that would tell you now you have stolen 170 from me, so since i don;t know yet til end of day when i tally up my register that i am missing 100 dollars, and so with that 100 dollars you stole and then handed it to me m i gave you back 30 dollars, so truth is you stole 200 from me, But i know why you came up with this answer, You snowflakes think everything is free, And so this is more fake news, don't worry trump will still be your president til 2024

  49. Hi, it is just a cuestion of taking in consideration if the the sell is depending on the robbery, but if no mentioned at first, must no depend on it

  50. i think the answer should be 200…cause if the thief had bought the goods with his own money…..then the owner would have gained 70 …also he has guven 30 on something bought frm his own money……so total loss 100+70+30=200

  51. Potential profits also don't matter guys. Let's say he only paid 50 dollars for that 70 dollar item. Let's say the owner has 100 dollars before this transaction so he now has 50 in his bank account. If someone bought the item legit (and he marked it up to 70 like I said to gain profit) he would now have 120 dollars in his bank account.

    Then we look at the thief. thief bought the item so normally he should have 120 dollars, but he stole 100 originally and the owner has to make up for that with his own money leaving him with 20 dollars in his bank account. leaving him out 100 dollars still. He still made the exact same profit margin because it was a real purchase, but it doesn't change the fact that all the thief stole was his 100 dollars. You guys are all complicating the cornflakes.

  52. Just think about it this way: if the guy who stole starts at 0, the money he ends up with is the money the owner lose, since the guy walks away with staff thats worth 70 + 30 dollars, thats what the owner has lost

    P.d: I am not a native so I hope you undertand if theres some grammar or spelling mistake dont judge me

  53. How much money did he lose? He lost $30 in cash. He also lost some goods, of which we don't know the value to the owner (although we do know the value of his price tags).

    But the question only asked how much money he lost, not the replacement value of the goods he lost, so strictly the answer is he lost $30 of his money.

  54. It can be 200$ as 100$loss is due to 70$ purchase and 30$exchange .
    But If that bill was given to another customer the other customers also purchase goods of that price

  55. That problem doesn’t make sense in your 2nd misconception because the robber stole $100 and then use the same stolen money to buy only $70 worth of stuff and get
    $30 back in change? The owner still lost money more than $100 because the robber is refusing assets to gain more property from the store than originally intended.

  56. I have a similar problem for you:
    3 men are in a bar and buy drinks. They have to pay 25$, but have only a 10$bill each, so they give the barman 10$ each, so they pay 3×10$=30$. The barman gives back 5 coins of 1$. The 3 guys take 1$ each and leave 2$ as a tip.
    So, each of them have pay 10$-1$=9$, that makes 27$. You add 2$ from the tip, that make it 29$. But they gave initialy 30$! Where is the last $ gone????!!!

  57. The answer is $30. That's how much money he lost in that moment. The "goods" (products) are not money.

  58. Steals $100, owner now -$100.
    Buys $70 worth of goods with the same $100. How does the owner get the $100 restored if the man had use the same $100 but for a different transaction. Then the owner manages to give the man another $30 for change. The $70 the man paid for out of the $100 he gives back was now wasted for another purpose so the owner does not profit from it. Making it still -100 because Tht bill came from past transactions and now the owner is down -100 from his past transactions in addition towards the $70 worth of products he lost and $30 he gave for change.

  59. Basically the $100 was stolen from past transactions and now it’s being used for a different transaction.

  60. The thief steals a $100 bill on Monday.
    On Tuesday he buys $70 worth of goods. He pays with two $50 notes and gets his $30 change.
    The events of Monday and the events of Tuesday have nothing to do with each other.

  61. I still don’t get it because in essence at the end when the register is counted, it will be missing 100 then upon realizing the lost to productivity you will be down 100 plus the 30 in change and 70 in product which would be 200

  62. idk
    first the owner loses $100 (stolen from the store)
    second the owner loses $70 (Goods given to the guy)
    Third the owner loses $30 (Change given to the guy)
    Isn't that $200 in all ? (just my thought)

  63. Hey, just wanted to comment that although the goods cost to the owner less than $70, his/her intention was NOT for they to left in the store but rather be bought by customers for a total of $70, therefore they aren't REALLY worth less than $70.

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