While walking in a park, one morning, I found a Hundred Rupee note on one of the park benches. I picked it up, noted the number and took it home.

In the afternoon the plumber called on me to collect his bill. As I had no other moey at home, I settled his account with the Hundred Rupee note that I had found.

Later I came to know that the plumber paid the note to his milkman to settle his monthly account , who paid it to his tailor for the garments he had made.

The tailor in turn used the money to buy an old sewing machine, from a woman who lives in my neighbourhood. This woman incidentally, had borrowed Hundred Rupees from me sometime back to buy some household appliance. She, remembering that she owed me a Hundred Rupees, came and paid the debt.

I recognized the note as the one that I had found on the park bench, and on careful examination, I discovered that the note was counterfeit.

How much was lost in the whole transaction and by whom ?

First, ignoring for the moment the incident where Ravi found the note, and the one where he discovered it was counterfeit, consider only the commercial transactions.

This part of the problem is very similar to the problem "A Drinking Problem," in which Ben owes Glen a drink, Glen owes Rhen, etc. In that case, the first person bought the second a drink; the second person passed that drink on to the third, etc. and everyone's debt was reduced one drink by that single drink.

Likewise, if Ravi had a real 100 rupee note, all the debts would have been satisfied.

Also consider if Ravi had a real 100 rupee note and placed it in an envelope. Then he gives the envelope to the plumber, and it follows the same path. When Ravi gets the envelope back from the neighbor lady, he realizes that he gave the plumber the wrong envelope and none of the others ever held the 100 rupee note. Does this make a difference? No -- Everyone is in exactly the same condition as at the end of the last paragraph.

It's the same here. No one gained or lost in this series of transactions.

But what about the opening and closing incidents? If Ravi found a 100 rupee note, he would be up 100 rupees. If he'd found a useless piece of paper, he would be neither up nor down.

If he found a 100 rupee note, either real or counterfeit, and spent it he would be up 100 rupees if it never came back to him.

But it did come back to him, and (except for the round of debts canceled) he was in the same situation as when he first found it. Upon discovering that it is not a genuine note, but a useless piece of paper, he discovered that he was not up 100 rupees as he had thought, but he didn't actually lose anything, though, either.

There was a time that he thought he was up 100 rupees, and discovering that it was not real felt like losing 100 rupees he thought he had, but mathematically, he broke even.

Posted by TomM on 2003-03-21 17:15:27