# Missing Dollar (A Classic)

geepamoogle
Posers and Puzzles 21 Feb '07 21:23
1. 21 Feb '07 21:23
The manager is working at a hotel one night when three men come in and ask for a single room for the night. The manager replies that the cost will be \$30, and each man puts in \$10 and they head up to their rooms. The manager begins to put the money in the register when he realizes he has overcharged the men by \$5, and asks a favor for the bellhop, who saw the men check in. The bellhop heads up to the room, when it occurs to him that \$5 doesn't evenly divide into 3, and comes up with a bright idea. He pockets \$2, and gives each man a \$1 bill back, the men being none the wiser.

Now the question is this.. We know that each man ends up paying \$9, accounting for \$27 of the original total and that the bellhop kept \$2, so where is the missing \$1?
2. 21 Feb '07 21:44
Originally posted by geepamoogle
The manager is working at a hotel one night when three men come in and ask for a single room for the night. The manager replies that the cost will be \$30, and each man puts in \$10 and they head up to their rooms. The manager begins to put the money in the register when he realizes he has overcharged the men by \$5, and asks a favor for the bellhop, who ...[text shortened]... ounting for \$27 of the original total and that the bellhop kept \$2, so where is the missing \$1?
There is no missing dollar, of course, because the question is misstated: The men each payed \$9, for a total of \$27, the bellhop essentially just took \$2 of that, and the remaining \$25 went into the cash register.

Only \$27 left the men's pockets, not \$30.
3. 22 Feb '07 01:49
Doesn't look like anyone else has anything to add. You, sir, are indeed correct.

The bad thing is, this problem was posed in some fluff (philosophy, I think) course at a technical school I was at, and tried to explain that the logical framing of the question was faulty, but I never could get the teacher to figure that out. Of course, it only works if you frame it that way, or else people naturally order it in a more consistent manner, and there ceases to be any riddle at all.

When you point out the \$27 paid, you are, in essence, pointing out where the money is NOT, rather than looking at where it IS.. The other \$3 are with the gentlemen, as a rebate.