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## Question

This seems simple, but I am amazed with different answers I receive. Here it is:

A Man (Mr. X) goes to grocer (Mr. Y) to buy a toothpaste. The grocer (Mr. Y) gives Mr. X the toothpaste and says it is \$4. Mr. X takes out his wallet and hands him \$10 bill. Now the grocer (Mr. Y) checks his cash register and finds that he has few \$10 Bills and two \$1 bills. So he sends his assistant to the next door shop owner (Mr. Z) to get change. The assistant hands over \$10 bill, which he got from Mr. X to Mr. Z. Mr. Z in turn hands him change of two \$5 bills. The assistant then hands that over to the Grocer Mr. Y. The Grocer puts one \$5 bill back in the cash register, takes out a dollar bill and along with the other \$5 bill, he hands \$6 back to our customer Mr. X along with the toothpaste. Mr. X walks away. After a few minutes, the next door shop owner Mr. Z turns up at the Grocer Mr. Y and complains that the \$10 bill his assistant gave was a fake one and of no use. Mr. Y being a nice grocer apologizes and hands another \$10 bill from his cash register to compensate to Mr. Z. So the question is : How much was the monetary loss and to whom ?

## 42 answers to this question

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Well, wouldn't Mr. X lose \$4 b/c he bought a toothpaste?

Why is Mr. Y reimbursing Mr. Z? Mr. Z gave 2 \$5 bills, not a \$10.

Edited by dawgsrule93

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Well, wouldn't Mr. X lose \$4 b/c he bought a toothpaste?

Expensive toothpaste - but not if you passed on a bad note, recieved change and a product too - which is one way to launder bad money

.

Nearly forgot to use spoiler. Sorry

Edited by Lost in space

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Mr X gets a \$4 toothpaste for free ... so it must be Mr. Y who lost \$4.

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might be jumping the gun, but I'd say \$20 total. \$16 in cash, and \$4 in merchandise.

Edited by Noct

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How much was the monetary loss and to whom ?

More information is needed. Did Mr. X counterfeit the money himself? If so, then he made \$10 (assuming it costs him nothing to produce a counterfeit bill). He has \$6 in his pocket and \$4 worth of toothpaste. Did he get passed the counterfeit money in another transaction and wasn't aware it was counterfeit? Then he made nothing and lost nothing. He exchanged a fake \$10 bill (which he worked for or received fairly, making it irrelevant that it was fake) for \$6 and \$4 worth of toothpaste.

Mr. Y is out \$10 as he assumed the responsibility for the fake (unless Mr Z is lying or incorrect) bill.

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More information is needed. Did Mr. X counterfeit the money himself? If so, then he made \$10 (assuming it costs him nothing to produce a counterfeit bill). He has \$6 in his pocket and \$4 worth of toothpaste. Did he get passed the counterfeit money in another transaction and wasn't aware it was counterfeit? Then he made nothing and lost nothing. He exchanged a fake \$10 bill (which he worked for or received fairly, making it irrelevant that it was fake) for \$6 and \$4 worth of toothpaste.

Mr. Y is out \$10 as he assumed the responsibility for the fake (unless Mr Z is lying or incorrect) bill.

But the question isn't asking who made money/broke even, so your first paragraph is irrelevant.

On another note

I'm changing my answer back to my original \$10 I had first put. He loses \$6 in cash, \$4 in merchandise. OR \$10 to Mr. Z, depending on how you look at it.

Edited by Noct

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This seems simple, but I am amazed with different answers I receive. Here it is:

A Man (Mr. X) goes to grocer (Mr. Y) to buy a toothpaste. The grocer (Mr. Y) gives Mr. X the toothpaste and says it is \$4. Mr. X takes out his wallet and hands him \$10 bill. Now the grocer (Mr. Y) checks his cash register and finds that he has few \$10 Bills and two \$1 bills. So he sends his assistant to the next door shop owner (Mr. Z) to get change. The assistant hands over \$10 bill, which he got from Mr. X to Mr. Z. Mr. Z in turn hands him change of two \$5 bills. The assistant then hands that over to the Grocer Mr. Y. The Grocer puts one \$5 bill back in the cash register, takes out a dollar bill and along with the other \$5 bill, he hands \$6 back to our customer Mr. X along with the toothpaste. Mr. X walks away. After a few minutes, the next door shop owner Mr. Z turns up at the Grocer Mr. Y and complains that the \$10 bill his assistant gave was a fake one and of no use. Mr. Y being a nice grocer apologizes and hands another \$10 bill from his cash register to compensate to Mr. Z. So the question is : How much was the monetary loss and to whom ?

']Well if you count full value for the toothpaste, Mr. Y lost \$10. (He received a fake \$10 bill and gave \$4 in merchandise and \$6 in change.)

Now the interesting questions are: Was there a fake \$10? (Mr. Y simply took Mr. Z's word!) If there was a fake \$10 where did it come from? (Mr. X, Mr. Y, the assistant (Mr. y?), or Mr. Z?

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More information is needed. Did Mr. X counterfeit the money himself? If so, then he made \$10 (assuming it costs him nothing to produce a counterfeit bill). He has \$6 in his pocket and \$4 worth of toothpaste. Did he get passed the counterfeit money in another transaction and wasn't aware it was counterfeit? Then he made nothing and lost nothing. He exchanged a fake \$10 bill (which he worked for or received fairly, making it irrelevant that it was fake) for \$6 and \$4 worth of toothpaste.

Mr. Y is out \$10 as he assumed the responsibility for the fake (unless Mr Z is lying or incorrect) bill.

hmmmm .... Mr. X also got a change of \$6 -- well, that will make it \$10 loss to Mr. Y

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']Well if you count full value for the toothpaste, Mr. Y lost \$10. (He received a fake \$10 bill and gave \$4 in merchandise and \$6 in change.)

Now the interesting questions are: Was there a fake \$10? (Mr. Y simply took Mr. Z's word!) If there was a fake \$10 where did it come from? (Mr. X, Mr. Y, the assistant (Mr. y?), or Mr. Z?

The fake \$10 bill came from Mr. X................

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Mr. Y is only out \$6 + cost of the toothpaste. It would not be \$4 otherwise he would not be in business. Probably closer to \$1 or \$2 or so. Mr. Y would be out \$7-\$8.

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So he sends his assistant to the next door shop owner (Mr. Z) to get change. The assistant hands over \$10 bill, which he got from Mr. X

The OP is pretty clear about the fake \$10 coming from Mr. X. So Mr. Y is out \$10 because he did everything properly. Nice guys finish last I guess.

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If the money was real, Mr. Y would have whatever cash he already had in his till plus \$4 more dollars (the cost of the toothpaste).

Mr. Y gets a fake \$10 intead, and exchanges it for 2 real \$5. Mr. X leaves with \$4 toothpaste and \$6 cash. Mr. Z is reimbursed \$10 real cash for the \$10 fake he received from Mr. Y. Mr. Y is therefore out \$10 in cash and \$4 in product for a total of a \$14 loss.

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Mr. Y is out \$6 + the cost of the toothpaste.

It's easy if you pretend that the fake \$10 bill doesn't exist:

Mr. Z gives Mr. Y \$10

Z is down \$10, Y is up \$10

Mr. Y gives Mr. X \$6 + toothpaste(\$t)

Z is down \$10, Y is up \$4 minus \$t, X is up \$6 and a tube of toothpaste

Mr. Y gives Mr. Z \$10

Z is even, Y is down \$6 and \$t, X is up \$6 and a tube of toothpaste

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Mr. Y is out \$6 + the cost of the toothpaste.

It's easy if you pretend that the fake \$10 bill doesn't exist:

Mr. Z gives Mr. Y \$10

Z is down \$10, Y is up \$10

Mr. Y gives Mr. X \$6 + toothpaste(\$t)

Z is down \$10, Y is up \$4 minus \$t, X is up \$6 and a tube of toothpaste

Mr. Y gives Mr. Z \$10

Z is even, Y is down \$6 and \$t, X is up \$6 and a tube of toothpaste

Well, about the cost of toothpaste idea. It depends on how you look at it. Say the toothpaste cost Mr. Y \$2. Then he'd be out \$8 bucks. But he already purchased the toothpaste at \$2, which is finalized before the riddle takes place. Now he expects to sell it for \$4, so that would make \$10. So is he out what he paid for the toothpaste or is he out for what he would sell the toothpaste?

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Mr. Z doesn't lose any money. He held a counterfeit \$10 bill for a time, but that's it.

(ie, breaks even)

Mr. X gave a counterfeit \$10 bill (costing him nearly nothing) and received \$6 and a \$4 tube of toothpaste.

(ie, gains \$10)

Mr. Y loses \$6 and a \$4 tube of toothpaste and gains a worthless \$10 bill

(loses \$10)

So, Mr. Y is the only one that loses money, and he loses \$10 worth of cash and merchandise (assuming he was to make no margin off the sale of the merchandise).

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Mr. X goes to Mr. Y to buy toothpaste.

Mr. Y gives Mr. X the toothpaste and says it is \$4.

Mr. X takes out his wallet and hands him \$10 bill. (Is that fake?)

Mr. Y checks his cash register and finds that he has few \$10 Bills and two \$1 bills.

Mr, Y sends his assistant to Mr. Z to get change.

Assistant hands over \$10 bill, which he got from Mr. X to Mr. Z. (Is that fake?)

Mr. Z hands him two \$5 bills.

The assistant then hands that over to Mr. Y.

Mr Y puts one \$5 bill back in the cash register,

takes out a dollar bill and along with the other \$5 bill,

hands \$6 back to Mr. X along with the toothpaste.

Mr. X walks away.

Mr. Z turns up at Mr. Y's and complains that the \$10 bill his assistant gave was a fake.

Mr. Y hands another \$10 bill from his cash register to Mr. Z. (is that fake?)

So the question is :

How much was the monetary loss and to whom ?

Simplified, but then when I read through and noticed in the OP a grocer selling toothpaste - does that happen?

Keep in mind the toothpaste retails at \$4 but is purchased at a lower cost price (whole sale)

Mr Z may have got the fake from any where,

so may be \$10 dollars better off than he was b4 the dubious assistant arrived.

(now at evens because he made good a loss from elsewhere unless he printed the fake - then he is \$10 better off.)

Mr X may have given the fake therefore he is \$10 better off (change and product)

Mr Y may have been given the fake anytime and lost \$10 dollar of product in the deal.

then he lost \$10 again taking mr Z's word for it.

There are fake notes going around and we should call the authorities - let them decide!

We can not assume there are no more fakes!

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The OP clearly states that the assistant hands Mr. Z the \$10 from Mr. X. If that is not the counterfeit 10, then we have to assume Mr. Z is lying and nowhere is anything said that should give that assumption.

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The grocer could have gotten the toothpaste for \$4 or \$5 or even more. Many times grocery stores will take no profit or a loss on some products to get customers into the store so they can make profit on other products.

But regardless, if he had sold the toothpaste to someone else, he would have grossed \$4, but since he practically gave it away, he is out \$4 that he would have normally gotten, plus the \$6 change for a total of \$10

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The grocer could have gotten the toothpaste for \$4 or \$5 or even more. Many times grocery stores will take no profit or a loss on some products to get customers into the store so they can make profit on other products.

But regardless, if he had sold the toothpaste to someone else, he would have grossed \$4, but since he practically gave it away, he is out \$4 that he would have normally gotten, plus the \$6 change for a total of \$10

If grocers sell toothpaste?

If the toothpaste is a loss leader/fly-catcher?

If it was X,Y,Z or assistant (getting off lightly - he's my bet)

Call the authorities and let them sort it out.

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This seems simple, but I am amazed with different answers I receive. Here it is:

A Man (Mr. X) goes to grocer (Mr. Y) to buy a toothpaste. The grocer (Mr. Y) gives Mr. X the toothpaste and says it is \$4. Mr. X takes out his wallet and hands him \$10 bill. Now the grocer (Mr. Y) checks his cash register and finds that he has few \$10 Bills and two \$1 bills. So he sends his assistant to the next door shop owner (Mr. Z) to get change. The assistant hands over \$10 bill, which he got from Mr. X to Mr. Z. Mr. Z in turn hands him change of two \$5 bills. The assistant then hands that over to the Grocer Mr. Y. The Grocer puts one \$5 bill back in the cash register, takes out a dollar bill and along with the other \$5 bill, he hands \$6 back to our customer Mr. X along with the toothpaste. Mr. X walks away. After a few minutes, the next door shop owner Mr. Z turns up at the Grocer Mr. Y and complains that the \$10 bill his assistant gave was a fake one and of no use. Mr. Y being a nice grocer apologizes and hands another \$10 bill from his cash register to compensate to Mr. Z. So the question is : How much was the monetary loss and to whom ?

Mr. Y loses 10\$.

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Mr Y is minus 6\$+the cost of the tootpaste,which for him is less then 4\$(but he could sell it to other client for 4\$).Let say Mr.Y had 22\$,Mr.X gives him 10\$(now Mr.Y has 22+10=32\$),which Mr.Y changes for 2*5\$ to Mr.Z and gives back to Mr.X one 5\$+1\$ from the register(32-6=26\$).Mr.Z comes and asks for 10\$,because the 10\$ are fake and Mr.Y gives to him another 10\$(26-10=16\$).Before Mr.X to come Mr.Y had 22\$ + tootpaste,after he left Mr.Y has 16\$ and he is minus 1 tootpaste.Total lost 6\$ and the cost of the tootpaste.

Edited by ash013

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If the money was real, Mr. Y would have whatever cash he already had in his till plus \$4 more dollars (the cost of the toothpaste).

Mr. Y gets a fake \$10 intead, and exchanges it for 2 real \$5. Mr. X leaves with \$4 toothpaste and \$6 cash. Mr. Z is reimbursed \$10 real cash for the \$10 fake he received from Mr. Y. Mr. Y is therefore out \$10 in cash and \$4 in product for a total of a \$14 loss.

You forgeting,that Mr.X kept 4\$,that's why his lost in cash is 10-4=6\$.

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Well, about the cost of toothpaste idea. It depends on how you look at it. Say the toothpaste cost Mr. Y \$2. Then he'd be out \$8 bucks. But he already purchased the toothpaste at \$2, which is finalized before the riddle takes place. Now he expects to sell it for \$4, so that would make \$10. So is he out what he paid for the toothpaste or is he out for what he would sell the toothpaste?

It doesn't matter what he WOULD have gotten, he is out the cost that it takes him to replace it (which may be \$4 and may not). If I own a car that is worth \$1000 and I try selling it for \$15,000 and it gets stolen, do you think the insurance company is going to give me \$15,000 because that's what I would have gotten had someone bought it?

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It doesn't matter what he WOULD have gotten, he is out the cost that it takes him to replace it (which may be \$4 and may not). If I own a car that is worth \$1000 and I try selling it for \$15,000 and it gets stolen, do you think the insurance company is going to give me \$15,000 because that's what I would have gotten had someone bought it?

Well, we don't know his whole sale price or mark up, so we can only guess which is pointless cos we will never know! It is only a fact that this may be part of the loss. Previous week it may have been part of an offer, or the whole sale company gave the guy a deal which made it free or.....etc

You may only get what the insurance wants to pay you for the car or you may challenge for more - I did and got more.

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As I said, the answer is no brainer, but I was amazed when I put this problem in my class with intelligent student. I had made it simple here, but in the original puzzle, the amount was a little higher and the transaction included couple of items, but I got answers ranging from \$10 to \$100.

Also, almost majority of my student came up with one answer instinctively and then changed it latter on.

Brhan intially got \$4 then changed to \$10

NoOct intially got \$20 then changed to \$10

Smokiecat intitally got \$14 then changed to \$10

Scraff, redshift, niner, itachi-san, eventhorizon, imran, ash013 all got \$10

Do I still need to spell out the answer ?...

Thanks

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