Wednesday, November 30, 2005

 

Mystery Of The Missing Dollar, Plus Monty's Doors.

Dean put up a perennial favorite of his, the puzzle of Monty's Doors. It one that seems to cause debate every time he posts it. Fortunately, I remembered it from last time, so this time I could enjoy it as an unconfused observer. Kind of more fun that way. However, this time, only one person disputed the correct answer, and that was because he misread the problem. Perhaps the bloom is off of the Monty's Doors rose. Which made me wonder about an old favorite from my youth. Has it held up? Does everyone see through it? You be the judge:

Three men go to a hotel. The clerk says the room is $30, and each man puts up $10. After they go upstairs, the clerk realizes he overcharged his guests, and the room actually only cost $25. Clerk calls Bellhop over, and tells him to take the $5 change up to the room and return it to the men. Bellhop decides it's too difficult to divide $5 among the three men, and his tips haven't been what they should be lately, so he keeps $2 for himself, and returns $1 each to the three men. $10 paid - $1 returned means each man has only paid $9 for the room. $9 x 3 men = $27. Bellhop kept $2. $27 + $2 = $29. What happened to the missing dollar?


Thanks again to Andrew for the help on the gleeking vs yanging question, and to any of you who might have chipped in on that one as well.
Comments:
This one gets me because while I know it's a trick, I can't articulate it very well.
 
This isn't so difficult to figure out. As a matter of fact, the trick is staring you right in the face. Any hotel that charges only $10 a head would never give back 5 bucks to 3 suckers who agreed to the higher price.
 
The solution is that $25 + $5 is $30. What happens to the funds after that doesnt' matter. The bellhop takes two dollars and returns three, so it's still $5 + $25.
 
There's no dollar missing; you're just being misled. At the end of the question, the $27 is added to the $2, but these are things which shouldn't be added together.

The men paid $27 and kept $3. Who got the $27? The hotel got $25. The bellhop got $2. $27=$25+$2. So, the $2 is already included in the $27; why would you add the $2 to the $27 again?
 
The fallacy is in the initial division. If a room is $25/night - then each man should have paid $8.33 (one would have to pay $8.34) each. Which means that the bellhop additionally shorted each man 67 cents (or 66ยข for the $8.34 guy).
 
Accounting majors should pick up on this right away.

Initially, the men have collectively paid $30 each, with the hotel receiving $30.

After the refund, the men have collectively paid $27, with $27 going to the hotel and bellhop.

The mistake is comparing the amount paid by the men in the end with the amount initially received by the hotel.

In table form:

Before initial Payment:
Men: $30
Hotel: $0
Bellhop: $0
Total: $30

After initial payment:
Men: $0
Hotel: $30
Bellhop: $0
Total: $30

After refund and tip:
Men: $3
Hotel: $25
Bellhop: $2
Total: $30
 
As some of you noted, careful thinking carries the day. It's the the wording of the problem that creates the dilemma. The dollar really is there all along. Good job!
 
Geek.esq explained it magnificently.

The short answer is that at the end, the $2 should be subtracted from the $27, not added.

The guys paid $9 each for the $25 hotel room. Of the $27 paid, the hotel got $25 and the bellhop took $2. Nothing's missing.

Teri
 
ok here the real thing

noobs

25$ for the room 3$ back to each man

they work it out to be 29$

but as a matter of fact its 28$+2$ bellhop has is 30$

witch is how they try to trick the gullible noobs that think tht they
paid 9$ each wen they paid 8.333333333etc $ each witch then adds up to be 25$ 2$ bell hop 1$ each man they is ur answer :)_
 
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