Maegan, I won’t make any judgment on whether you’re nuts or not (instinct of self-preservation and all that), but here’s how the whole transfer of money and products in this riddle goes:

1.  At the start, the buyer has the fake $20, the seller has the $10 hat, and the neighbour has $20 dollars:
B = $20 (fake)
S = $10 (the hat)
N = $20

2.  The buyer gives the fake $20 to the seller:
B = $0
S = $30 (the hat and the fake $20)
N = $20

3.  The seller gives the fake $20 to the neighbour:
B = $0
S = $10 (the hat)
N = $40 (including the fake $20)

4.  The neighbour gives $20 back to the seller:
B = $0
S = $30 (including the hat)
N = $20 (fake)

5.  The seller then gives the hat and $10 to the buyer:
B = $20 (including the hat)
S = $10
N = $20 (fake)

6.  The seller then has to give $20 to the neighbour:
B = $20 (including the hat)
S = $-10
N = $40 (including the fake $20)

The last part of the equations don’t seem right.  But the point is, the seller doesn’t have the hat, it was NEVER paid for.

The hat WAS paid for.  The buyer got R$20 from the changer and paid for the hat with R$10.  The equation looks right to me.

I know I’m nitpicky, but I still have an issue. The hat seller had to have originally paid for or used materials he paid for the make the hat. So, he’s kinda out of that money too.

Charybdis - 29 August 2005 03:38 PM

The hat WAS paid for.  The buyer got R$20 from the changer and paid for the hat with R$10.  The equation looks right to me.

No, the buyer got a FAKE $20, which he exchanged for a real $20.  The buy never got any payment for the hat.  Hence, the hat was never paid for.

Okay, if I went into a gas station, and I bought a coke that cost $1, and I gave the cashier a FAKE $1 bill - then I have the coke, and the cashier got nothing.  This is essentially what happened in this riddle, except change is made.  If you look at it like that, then the cashier is out $1 and a coke.

From what I understand of the riddle, the person who changed the money, was simply another vendor.

Winna, the ten dollar value of the hat would have covered the seller’s expenses of either making or else buying the hat.  So those costs are included in the twenty dollars he lost.

And Maegan, in your example, the cashier is not out $1 and the coke.  The fake $1 wasn’t his in the beginning, so he’s not lost that.  All he’s lost is the $1 value of the coke.  And you, as the customer, would have neither gained nor lost anything (assuming that you thought that the fake $1 was genuine).  You’d have lost the fake $1, but have gained $1 worth of drink.

The seller does not lose the hat, because it is paid for with with real money. The money that the helper gave the neighbor is fake, but the money the neighbor gives back is real. Therefor, the hat is not lost because it is paid for with legitimate money. The only money lost is the $20 that the seller gives to the neighbor.

Maegan, what if I just stole your coke from you.  You’re out $1 for the value of the coke.  If I gave you a dead snail for it, you’re only out $1.  If I gave you Monopoly money you’re still out only $1.  And lastly, if I gave you a counterfeit $1 bill then you’re still only out $1.

If the $20 was real then everybody would be happy and nobody would be out anything.  Since the $20 was fake somebody (the seller) is out $20, no more and no less.  You can’t be out more than the replacement value of the fake $20.  Even if you brought a thousand people into it and every single one of them passed the fake $20 off to somebody else, in the end the maximum total outage will be $20.

mooo1 - 29 August 2005 06:10 PM

The seller does not lose the hat, because it is paid for with with real money.

No, the hat is paid for with fake money.

mooo1 - 29 August 2005 06:10 PM

The money that the helper gave the neighbor is fake, but the money the neighbor gives back is real.

  Exactly, but the seller keeps none of this money.  The buy makes out with an extra $10 (b/c he never had any money to begin with.

mooo1 - 29 August 2005 06:10 PM

Therefor, the hat is not lost because it is paid for with legitimate money. The only money lost is the $20 that the seller gives to the neighbor.

  Look at it like this.  You are the buyer.  You knowingly hand a fake $20 to the seller.  Seller disappears with your fake $20 and shows up again with your “change” - a $10 bill, and your hat.  You leave with a hat and a real $10.  YOU NEVER PAID FOR THE HAT. 

Now, if you are the SELLER, someone approaches, gives you a $20, you provide them change (which yougot by trading the large bill for smaller amounts) - $10 bill, and their hat.  You believe the hat is paid for.

You are the NEIGHBOR/Changer.  Someone wants to know if you have change for a $20.  Sure, you give them some smaller bills.  Well, you relize, “Hey, this is so not real.”  You find the Seller, and ask for $20.

Okay, so the Changer got every penny of his money back.  The Buyer got his hat, and $10.  The Seller has a FAKE $20 which did not pay for the hat, and which is worthless to him, he also had to find $10 of his own money to return the whole $20 to the Changer.

Here’s one more attempt to show how the change of money and goods in this riddle goes.

It’s easier with her coke example. 

If I sell you a coke for $1 and it’s fake I’m out 1 coke.  I’m not out the 1$ because it never went anywhere.  You don’t have it, all you have is a coke.  There isn’t anyone else who could have it, therefore I must not be out it.