The Missing Pound

[steepholm]

First, let me say right out that I have never had any trouble with the Monty Hall problem.

I needed to say that, because I'm about to admit to yet another embarrassing deficit. When I was very young, I owned a book of puzzles, and one of them stumped me. It went like this....

Three men check into a hotel, and are charged £30 pounds in total for three single rooms. They pay the money and go to their rooms, but the receptionist later realizes that they should only have been charged £25 between them (it was a special offer). She calls the porter over, hands him the extra £5, and tells him to refund the guests. The porter however, confused no doubt the difficulty of dividing £5 in three, decides to pocket £2 and hand over £1 each to the guests.

So, in effect the guests have each paid £10-1=£9 (i.e. £27 in total), and the porter has pocketed £2, making £29. What happened to the extra pound?

I'd totally forgotten this puzzle, and the frustration it caused me, until I read it again the other day. It's driving me crazy! Put me out of my misery, someone.

Comments

[mraltariel.livejournal.com]

It is the "in effect" that is the problem. From the 30 pounds, They paid 25 pounds to the hotel, 2 pounds to the porter and 3 pounds back to themselves.

So, from each original 10 pounds they put into the pool:

8 1/3 pounds each goes to the hotel
2/3 pound goes to the porter
1 pound goes to themselves

The £10 - £1 calculation disguises the fact that their original £10 was actually sliced up three ways, not two, and you've not reassembled all three pieces in yur final sum.

[steepholm.livejournal.com]

Yes. I see that now. Tomorrow may be another matter, but thanks!

[swisstone.livejournal.com]

I think ... there is no extra pound. The £2 that the porter has pocketed is part of the £27 that the men have paid, and should not be added to it. Of that £27, £25 goes to the hotel, and £2 to the porter. The £3 difference between the £27 and the £30 is the £3 that the porter gave back to the men.

[steepholm.livejournal.com]

If I hold my head very steady, I think I can just see that. I don't guarantee that I will do so by tomorrow, but for now, much thanks!

[calimac.livejournal.com]

Answer. (in dollars, sorry)

[steepholm.livejournal.com]

The currency conversion makes surprisingly little difference, in this case. Thanks! I am no more in dumb amazement lost.