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.
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.
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.
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
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 $9.
I think everyone is correct however if we think about it 30-3+2รท9=27.2222222222 meaning the busboy had to keep the 2dollars because how would he give that in change
The explanation is perfectly fine. You should subtract 2 and not add 2 . See that the 5 dollars are -5 and not plus 5 , now you divide -5 into -3 + -2 not -3 + 2 which equals -1 , hence your missing 1.so 30-3-2=25. Not 30-3+2=27.
The travelers initially paid a total of 30$. The hotel discounts $5. So in reality they SHOULD have paid $8.33 each = $25. They end up paying 9$ each = $27, ($0.66 too much each = rounded up to $2 in total) – the $2 that the bellboy kept. $2 (bellboy) + $3 (the money they got back) = $5 (from the hotel) – no missing money :-)
16 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.
Natache Crook says
February 17, 2020 @ 23:43
I think everyone is correct however if we think about it 30-3+2รท9=27.2222222222 meaning the busboy had to keep the 2dollars because how would he give that in change
Piyush Aggarwal says
April 29, 2020 @ 22:54
I think that there is no remaining dollar.
Asher says
February 18, 2021 @ 13:09
This looks complicated, but think it’s really easy.
Jeh Deh says
March 28, 2021 @ 15:10
Using game theory there is no riddle. Just overspending because a weasel told on himself. Check it out: (3-25) + (25-30) = (27)
So it is now the missing $2 joke.
Yo says
May 26, 2021 @ 22:15
The explanation is perfectly fine. You should subtract 2 and not add 2 . See that the 5 dollars are -5 and not plus 5 , now you divide -5 into -3 + -2 not -3 + 2 which equals -1 , hence your missing 1.so 30-3-2=25. Not 30-3+2=27.
kyle says
December 9, 2021 @ 11:58
I still don’t understand. It should work out any way you calculate it. I have battled why this won’t work.
Jei says
May 15, 2022 @ 15:31
It’s not $27 up to $29; it’s $27 down to $25. (It’s a joke because it goes down by $2, like a weasel under Earth.)
People get confused because they’re going the wrong direction.
Gezowina says
June 19, 2022 @ 08:09
The travelers initially paid a total of 30$. The hotel discounts $5. So in reality they SHOULD have paid $8.33 each = $25. They end up paying 9$ each = $27, ($0.66 too much each = rounded up to $2 in total) – the $2 that the bellboy kept. $2 (bellboy) + $3 (the money they got back) = $5 (from the hotel) – no missing money :-)
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