# is the missing dollar unanswerable **URL:** \ **Category:** Factual Questions\ **Created:** [March 1, 2000, 2:21am UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347 "2000-03-01T02:21:00Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![C\_K\_Dexter\_Haven](https://avatars.discourse-cdn.com/v4/letter/c/b2d939/32.png) [@C\_K\_Dexter\_Haven](https://boards.straightdope.com/u/C_K_Dexter_Haven)\ **Post date:** [March 3, 2000, 5:51pm UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/21 "2000-03-03T17:51:00Z")
The confusion comes in part from having three characters (hotel, men/women, and bellhop). If there were only two characters, the mystery would vanish immediately: Three men check in to a hotel, they each pay $10. The hotel clerk realizes the room should only cost $25, but doesn’t want to distribute the uneven amount, so gives $1 back to each person and the hotel keeps the extra $2. No problem: hotel has $25 + 2, men have paid $27. No one tries to convince you that the men paid $27 and the hotel kept $2, totalling only $29. However, this mathematical analysis fails to take into account tax. In fact, the extra dollar goes to the government. What’s really missing is that that bellboy should also have paid social security tax on the 2 he kept, about .14 … So where’s the missing $.14?? ---
**Author:** ![Kat](https://avatars.discourse-cdn.com/v4/letter/k/b19c9b/32.png) [@Kat](https://boards.straightdope.com/u/Kat)\ **Post date:** [March 4, 2000, 2:29am UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/22 "2000-03-04T02:29:00Z")
In the version I read, the total comes to $63.50, and you have to account for the extra $33.50. But, come to think of it, it doesn’t mention Social Security tax… [Click here and scroll down](http://fathom.org/teemingmillions/pofunnies.adp) ---
**Author:** ![TBone2](https://avatars.discourse-cdn.com/v4/letter/t/6a8cbe/32.png) [@TBone2](https://boards.straightdope.com/u/TBone2)\ **Post date:** [March 4, 2000, 3:39am UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/23 "2000-03-04T03:39:00Z")
PEOPLE! The “three guys in a rented room” story is a thing of beauty! It has spanned generations and confounded millions! But the secret of it – the KEY – is in its telling! NOT in the math or the algebra or in trigonometry or any other studious pursuit. IT’S IN THE TELLING! ## One of the hundreds of reasons I have for loving my dad is the fact that he pestered the shit out of me with that riddle for years… _I don’t know why fortune smiles on some and lets the rest go free…_ T ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [March 4, 2000, 5:45am UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/24 "2000-03-04T05:45:00Z")
> [@](#): > > 2 x $14.00 = $28.00 plus the $3.00 that the bellboy kept makes $31.00. This is where you went astray, Henry. The three dollars that the bellboy kept came from the twenty eight dollars the two women paid. So why add it back in? The correct equation is “2 x $14.00 = $28.00 plus the $2.00 that the bellboy returned to the women makes $30.00.” ---
**Author:** ![siva](https://avatars.discourse-cdn.com/v4/letter/s/7c8e57/32.png) [@siva](https://boards.straightdope.com/u/siva)\ **Post date:** [March 9, 2000, 12:43pm UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/25 "2000-03-09T12:43:00Z")
I always thought it didn’t work because of the fraction involved. After the three guys paid $10 the three of them got $5 back total. The refund is 1.66 each. So subtract the 1.66667 from the original $10 that each guy paid for the room and you have 8.33. If the bellhop got tipped two bucks that means each person pays the bellhop .66 which in turn leaves each person $7.67. 7.67 multiply that by the three guys and you get $23.01. Add the 2 and you get 25.01 that they pay for the room, thats pretty darn close to the $25. The riddle is decieving cuz it doesnt account for the fraction—right? ---
**Author:** ![siva](https://avatars.discourse-cdn.com/v4/letter/s/7c8e57/32.png) [@siva](https://boards.straightdope.com/u/siva)\ **Post date:** [March 9, 2000, 12:47pm UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/26 "2000-03-09T12:47:00Z")
Ohh geez i forgot to say this. after the 5 rebate that left each person 8.33. The 33 cents is whats missing. .33 x 3 =$1 ---
**Author:** ![C\_K\_Dexter\_Haven](https://avatars.discourse-cdn.com/v4/letter/c/b2d939/32.png) [@C\_K\_Dexter\_Haven](https://boards.straightdope.com/u/C_K_Dexter_Haven)\ **Post date:** [March 9, 2000, 1:18pm UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/27 "2000-03-09T13:18:00Z")
OK, so the three guys paid $30. The hotel kept $25, that’s $55. The bellboy kept $2, that’s $57. The bellboy gave $3 back to the guys, that’s $60. The three guys each got back $3, that’s $63. So the three guys really paid $9 each, that’s $27 more, added to the $63 gives $90. Where did the other $60 come from? The whole question is easy if you say the hotel is in Sweden, since then the taxes account for the extra money, very quickly. Sheeeeeeeeesh. ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [March 9, 2000, 3:01pm UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/28 "2000-03-09T15:01:00Z")
Dex That’s gotta go in the rec.puzzles archive! Permission to reproduce? With attribution where possible. * * * rocks ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [March 10, 2000, 6:38am UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/29 "2000-03-10T06:38:00Z")
Siva, let’s make one more attempt here. Get thirty dollars and five envelopes. If you don’t have thirty dollars, use thirty pennies or buttons or matchsticks and pretend. Label the envelopes customer 1, customer 2, customer 3, bellboy, and hotel. Draw faces on them if you wish to personalize the whole thing. Now go through the problem step by step and move the dollars from envelope to envelope as you do so. Hopefully by the time you are done you will have acheived enlightenment and will now understand that there was never more or less than thirty dollars at any point. ---
**Author:** ![andyrose](https://avatars.discourse-cdn.com/v4/letter/a/ccd318/32.png) [@andyrose](https://boards.straightdope.com/u/andyrose)\ **Post date:** [July 19, 2002, 4:21am UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/30 "2002-07-19T04:21:39Z")
A friend told me that it had to do with limits and trigonometry. ---
**Author:** ![tomndebb](https://avatars.discourse-cdn.com/v4/letter/t/b9e5f3/32.png) [@tomndebb](https://boards.straightdope.com/u/tomndebb)\ **Post date:** [July 19, 2002, 4:28am UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/31 "2002-07-19T04:28:30Z")
> [@](#): > > it had to do with limits and trigonometry. I presume that this was because the three customers had to cosine for the room? (Or am I going off on a tangent?) ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [July 19, 2002, 4:39am UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/32 "2002-07-19T04:39:31Z")
No, you just have to look at the problem from the right angle. ---
**Author:** ![andyrose](https://avatars.discourse-cdn.com/v4/letter/a/ccd318/32.png) [@andyrose](https://boards.straightdope.com/u/andyrose)\ **Post date:** [July 19, 2002, 5:08am UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/33 "2002-07-19T05:08:14Z")
> [@](#): > > \*Originally posted by tomndebb \* > \*\*I presume that this was because the three customers had to cosine for the room? (Or am I going off on a tangent?) \*\* Very nicely done. ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [July 19, 2002, 5:50am UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/34 "2002-07-19T05:50:07Z")
I think the limit part was because of the innkeeper’s L’Hospitality. ---
**Author:** ![sturmhauke](https://avatars.discourse-cdn.com/v4/letter/s/e47c2d/32.png) [@sturmhauke](https://boards.straightdope.com/u/sturmhauke)\ **Post date:** [July 19, 2002, 10:23am UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/35 "2002-07-19T10:23:22Z")
Oh god, calculus jokes. [Arthur, King of the Britons] Run away! [/Arthur] Look, the riddle doesn’t have anything to do with limits or trig or fractions. Think of it this way: the amount that the three guests paid is a negative amount of money, while the amout that the attendant has is a positive amount of money. The riddle tricks you into thinking that the amount the guests paid is positive also. Put another way, you can’t add money someone doesn’t have to money someone else does have and get a number that makes any sense. ---
**Author:** ![Philster](https://avatars.discourse-cdn.com/v4/letter/p/13edae/32.png) [@Philster](https://boards.straightdope.com/u/Philster)\ **Post date:** [July 19, 2002, 1:44pm UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/36 "2002-07-19T13:44:43Z")
Look, if a chicken and a half, rents a room and a half, for a dollar and a half, how long will it take a monkey with a wooden leg to kick all the seeds out of a dill pickle? ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [July 19, 2002, 1:59pm UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/37 "2002-07-19T13:59:33Z")
Um… four. ---
**Author:** ![NurseCarmen](https://avatars.discourse-cdn.com/v4/letter/n/5daacb/32.png) [@NurseCarmen](https://boards.straightdope.com/u/NurseCarmen)\ **Post date:** [July 19, 2002, 3:41pm UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/38 "2002-07-19T15:41:33Z")
The crux of the riddle lies in trying to find a room in New York City for $30 a night, much less $25. It is due to this hurdle that the greatest scientific minds of the world have been unable to come up with an acceptable answer. ---
**Author:** ![RiverRunner](https://avatars.discourse-cdn.com/v4/letter/r/977dab/32.png) [@RiverRunner](https://boards.straightdope.com/u/RiverRunner)\ **Post date:** [July 19, 2002, 7:23pm UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/39 "2002-07-19T19:23:48Z")
> [@](#): > > \*Originally posted by Philster \* > \*\*Look, if a chicken and a half, rents a room and a half, for a dollar and a half, how long will it take a monkey with a wooden leg to kick all the seeds out of a dill pickle? \*\* A toothbrush, 'cause motorcycles don’t have seat belts. RR ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [July 19, 2002, 7:54pm UTC](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347/40 "2002-07-19T19:54:07Z")
> [@](#): > > Now if each paid $10 and each got a $1 refund that equals $9 that each person paid for that 1 room. Right. $30 - $3 = $27. > [@](#): > > The attendant got a two dollar tip. Right. And $27 - $2 = $25, which is the room’s actual cost. > [@](#): > > $27 plus $2 equals $29. Yes, but so what? They didn’t tip the $2 from the $29. They tipped the $2 from the $5 refund. > [@](#): > > What happened to the other dollar? There is no “other dollar”. $2 + $3 + $25 = $30 [Previous page](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347.md?page=1) [Next page](https://boards.straightdope.com/t/is-the-missing-dollar-unanswerable/8347.md?page=3)