## The Missing Dollar

Three travelers register at a hotel and are told that their rooms will cost $10 each so they pay $30. Later the clerk realizes that he made a mistake and should have only charged them $25. He gives a bellboy $5 to return to them but the bellboy is dishonest and gives them each only $1, keeping $2 for himself. So the men actually spent $27 and the bellboy kept $2. What happened to the other dollar of the original $30?

There is no missing dollar from the original $30 because after getting $1 back, the three travelers had paid a total of $27 for their room ($9 each), not $30. Out of that $27, the hotel has $25 and the clerk kept the remaining $2. If you still want to work from the original $30, the travelers have $3, the hotel has $25 and the bellboy has $2. The misleading part is adding the bellboy’s $2 to the $27, when in fact it should be subtracted.

7 Comments on "The Missing Dollar"Isuzu says

October 12, 2015 @ 03:08

Good Explanation!!

Logical Puzzles

Daniel Kim says

September 5, 2016 @ 06:14

This is dumb what kind of answer is that, there is no missing dollar, actually the question is dumb, the answer was completely fine!

Justin says

November 4, 2018 @ 23:31

The funny thing about this is that the distribution of the funds makes sense… $25 to the hotel, $3 back to the men and $2 in the clerk’s pocket. Such a distribution is sound and adds up to $30 and therefore indicates that no money is lost.

However, the puzzle is not related to the distribution, but the fact that adding the amounts back using our current mathematical system does not “reverse-check” any way you try to do it. The men originally spent $10 each. Getting a dollar back means, with mathematical certainty, that each man then only spent $9. Three times 9 = 27. Add the 2 that was pocketed by the clerk and you end up with $29. THIS is the puzzle and it is not solvable.

Justin says

November 5, 2018 @ 07:15

Haha. I retract my previous statement. It fooled me for a minute, too. Yes, recognizing that the 2 needed to be subtracted from the $5 being given back and not added to the 27 that the men spent helped me grasp the correct point of view.

Brandon says

December 22, 2018 @ 15:09

I heard this on a school field trip about 15 years ago. It’s all about telling a story. Seeing the riddle in a few sentences ruined it. The math is simole but the story can be misleading

2 truth's says

January 31, 2019 @ 01:27

Both truth’s are equally true at the same time

Pamini Rathore says

December 23, 2019 @ 19:29

The whole confusion is in multiplication. Initially you multiply $10 x 3 = $30 but since $1 was returned to each guest, the actual multiplication changes from $10 to $9, hence the latter multiplication would be $9 x 3= $27 + $2 tip to waiter, which makes it to $29. Hence there is no missing dollar, the entire illusion was created with keeping original $10 multiplication instead of latter changing it to $9.

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