# Is there an answer?

golfer1
Posers and Puzzles 24 Apr '08 22:29
1. 24 Apr '08 22:29
A friend of mine told me this riddle, and I'm trying to figure out an explanation for why this happens. Here goes:

Three guys walk into a hotel and get a room. The room is \$30, so each guy coughs up \$10. After they go up to their room, the manager realizes that he overcharged them for the room. He opens up the register, takes out a \$5 bill, and tells one of his employees to take it up to the room. On his way up there, the guy realizes that they can't possibly split \$5 between three guys. He takes out his wallet, puts the \$5 bill in it, and takes out three \$1 bills. He keeps \$2. Each guest gets \$1. Now it's like they each paid \$9 for the room. \$9 x 3 guys = \$27, \$27+ \$2 (the money the employee kept for himself) = \$29.

Where'd the missing dollar go?
2. 24 Apr '08 22:32
The \$2 is included in the \$27, so you shouldn't add it again. \$25 with the hotel, \$2 with the guy, and \$3 with the other guys = \$30.
3. 24 Apr '08 23:03
This particular problem is deceptive (and intentionally so) because it gives you a logic that has an inconsistent frame of reference.

So let us examine the facts, then process into the account, shall we?

To simplify things, the three men will be considered a single party, as there really isn't anything distinguishing one from the other.

1) The Men pay the Manager \$30.
2) The Manager hands the Bellhop \$5.
3) The Bellhop hands the Men \$3.

Three transactions, now let us track where the \$30 is

Before step one, the Men have \$30, and the Manager and Bellhop have \$0 each.

After payment, the Manager has \$30, and the Bellhop and Men \$0.

After the Manager tasks the Bellhop, the Manager has \$25 (NOT \$27), the Bellhop \$5, and the Men \$0.

After the Bellhop performs the incomplete refund, the Manager still has \$25, the Bellhop \$2, and the Men \$3. Sum total is \$30.

So as the second poster has pointed out, the \$27 paid includes both the Manager's revenue and the Bellhop's "fee", and the remaining \$3 is back with the men.
4. wolfgang59
surviving
25 Apr '08 15:25
Originally posted by golfer1
A friend of mine told me this riddle, and I'm trying to figure out an explanation for why this happens. Here goes:

Three guys walk into a hotel and get a room. The room is \$30, so each guy coughs up \$10. After they go up to their room, the manager realizes that he overcharged them for the room. He opens up the register, takes out a \$5 bill, and tells one ...[text shortened]... \$27+ \$2 (the money the employee kept for himself) = \$29.

Where'd the missing dollar go?
Obviously the maid got it.
5. 25 Apr '08 16:08
Originally posted by wolfgang59
Obviously the maid got it.
The maid made a buck...
6. 27 Apr '08 21:50
Originally posted by golfer1
A friend of mine told me this riddle, and I'm trying to figure out an explanation for why this happens. Here goes:

Three guys walk into a hotel and get a room. The room is \$30, so each guy coughs up \$10. After they go up to their room, the manager realizes that he overcharged them for the room. He opens up the register, takes out a \$5 bill, and tells one ...[text shortened]... \$27+ \$2 (the money the employee kept for himself) = \$29.

Where'd the missing dollar go?
30-5=25 with manager

5-3=2 with employee

1+1+1=3 with each of three guys

25+2+3=30

Why did you think there would be 29\$, I don't understand?
7. 27 Apr '08 23:05
Originally posted by UzumakiAi
30-5=25 with manager

5-3=2 with employee

1+1+1=3 with each of three guys

25+2+3=30

Why did you think there would be 29\$, I don't understand?
The problem is intentionally worded with false, inconsistent logic.

The person posing this intentionally counts the bellhop's \$2 separately from the \$27 the men paid (when it is actually a part of it), and intentionally ignores the \$3 they got back.

The problem is solved when the solver realizes this and frames the problem properly.
8. 27 Apr '08 23:10
Originally posted by geepamoogle
The problem is intentionally worded with false, inconsistent logic.

The person posing this intentionally counts the bellhop's \$2 separately from the \$27 the men paid (when it is actually a part of it), and intentionally ignores the \$3 they got back.

The problem is solved when the solver realizes this and frames the problem properly.
Oh. Strange.