# A riddle for the math nerds **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [August 15, 2002, 2:17pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020 "2002-08-15T14:17:15Z")\ **Posts on this page:** 14\ **Page:** 1
**Author:** ![captainolev](https://avatars.discourse-cdn.com/v4/letter/c/a9adbd/32.png) [@captainolev](https://boards.straightdope.com/u/captainolev)\ **Post date:** [August 15, 2002, 2:17pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020/1 "2002-08-15T14:17:15Z")
This is a riddle with on good answer that I have found try it out. Three business men go on a trip, they stop at a hotel for the night and split the cost of the room. The room cost $30 so they paid $10 each. One their way up to the room the manager at the front desk remembers their business men discount of $5. So the bell hop takes the five dollars up to the room, on the way he realises that it will not split evenly three ways so he pockets $2. When he reaches the room he give each man a dollar back. So each business man paid $9 for the room. $9 per business man times 3 business men equals $27 plus the stolen $2 equals $29. where is the missing dollar? ---
**Author:** ![Newton\_meter](https://avatars.discourse-cdn.com/v4/letter/n/57b2e6/32.png) [@Newton\_meter](https://boards.straightdope.com/u/Newton_meter)\ **Post date:** [August 15, 2002, 2:24pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020/2 "2002-08-15T14:24:05Z")
[http://www.straightdope.com/classics/a910621.html](http://www.straightdope.com/classics/a910621.html) ---
**Author:** ![Joey\_P](https://avatars.discourse-cdn.com/v4/letter/j/919ad9/32.png) [@Joey\_P](https://boards.straightdope.com/u/Joey_P)\ **Post date:** [August 15, 2002, 2:24pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020/3 "2002-08-15T14:24:48Z")
Add it correctly. The front desk has $25, the bellhop has $2 and the men have $3. That’s $30. It doesn’t work when you add how much they paid to how much was stolen. The riddle forces you to add incorrectly. ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [August 15, 2002, 2:27pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020/4 "2002-08-15T14:27:03Z")
First, the General Questions forum is for questions you don’t already know the answer to. Riddles (unless you don’t already know the answer) go in MPSIMS. I’ll move this over there. Second, some guy named **Cecil Adams** once wrote a column called [Riddle: The 3 guys, the bellhop, and the missing buck](http://www.straightdope.com/classics/a910621.html) ---
**Author:** ![captainolev](https://avatars.discourse-cdn.com/v4/letter/c/a9adbd/32.png) [@captainolev](https://boards.straightdope.com/u/captainolev)\ **Post date:** [August 15, 2002, 2:34pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020/5 "2002-08-15T14:34:07Z")
bibliophage I think you missunderstood me as far as knowing the answer I said I have not found a good one. That does not mean i know the answer. Joey P while the way you answer is correct the other way is also mathmaticaly correct as well. They did each pay $9 there where three men and the bellhop did steal $2. That is why i posted it there is no logical explaniation on this answer. ---
**Author:** ![Joey\_P](https://avatars.discourse-cdn.com/v4/letter/j/919ad9/32.png) [@Joey\_P](https://boards.straightdope.com/u/Joey_P)\ **Post date:** [August 15, 2002, 2:37pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020/6 "2002-08-15T14:37:20Z")
No it’s not correct, that’s why it doesn’t work. If it was correct it would work. ---
**Author:** ![captainolev](https://avatars.discourse-cdn.com/v4/letter/c/a9adbd/32.png) [@captainolev](https://boards.straightdope.com/u/captainolev)\ **Post date:** [August 15, 2002, 2:39pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020/7 "2002-08-15T14:39:24Z")
all i am saying is think about it more than one way it will start to drive you nuts cause it sounds viable. thats all. i like the bluntness joey p. ---
**Author:** ![Joey\_P](https://avatars.discourse-cdn.com/v4/letter/j/919ad9/32.png) [@Joey\_P](https://boards.straightdope.com/u/Joey_P)\ **Post date:** [August 15, 2002, 2:45pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020/8 "2002-08-15T14:45:54Z")
Here check these links to old questions if you don’t believe me. This was found doing a search for “bellhop” if check some of the other variations of the riddle I’m sure you’ll find more. [The Hotel Gry: Triple Room, $25/night](http://boards.straightdope.com/sdmb/showthread.php?threadid=126378&highlight=bellhop) [is the missing dollar unanswerable](http://boards.straightdope.com/sdmb/showthread.php?threadid=13188&highlight=bellhop) [I need the true answer to this riddle](http://boards.straightdope.com/sdmb/showthread.php?threadid=126375&highlight=bellhop) [A number riddle - where did the £1 go??](http://boards.straightdope.com/sdmb/showthread.php?threadid=107637&highlight=bellhop) [a math riddle](http://boards.straightdope.com/sdmb/showthread.php?threadid=68397&highlight=bellhop) [Riddle…Any takers?](http://boards.straightdope.com/sdmb/showthread.php?threadid=47609&highlight=bellhop) [HERES ONE FOR YOU](http://boards.straightdope.com/sdmb/showthread.php?threadid=43522&highlight=bellhop) [So old, can any one remember?](http://boards.straightdope.com/sdmb/showthread.php?threadid=41326&highlight=bellhop) [math problem](http://boards.straightdope.com/sdmb/showthread.php?threadid=32757&highlight=bellhop) [Help me with this riddle…](http://boards.straightdope.com/sdmb/showthread.php?threadid=2253&highlight=bellhop) ---
**Author:** ![Joey\_P](https://avatars.discourse-cdn.com/v4/letter/j/919ad9/32.png) [@Joey\_P](https://boards.straightdope.com/u/Joey_P)\ **Post date:** [August 15, 2002, 2:48pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020/9 "2002-08-15T14:48:09Z")
I’m a math major, so I don’t see much point in looking at anyways but the correct way. Math is all that philisophical to me until we get into alternate (non-euclidean) geometries. ---
**Author:** ![Joey\_P](https://avatars.discourse-cdn.com/v4/letter/j/919ad9/32.png) [@Joey\_P](https://boards.straightdope.com/u/Joey_P)\ **Post date:** [August 15, 2002, 2:49pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020/10 "2002-08-15T14:49:57Z")
That should say …math isn’t all that… ---
**Author:** ![Newton\_meter](https://avatars.discourse-cdn.com/v4/letter/n/57b2e6/32.png) [@Newton\_meter](https://boards.straightdope.com/u/Newton_meter)\ **Post date:** [August 15, 2002, 2:56pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020/11 "2002-08-15T14:56:50Z")
Accountants use _double entry_ accounting to make sure that they don’t make exactly the mistake that you are making (IANAA, so feel free to correct gross misconceptions). Every transaction is entered in two columns–one positive and one negative. That is, when you spend money (negative), it goes somewhere (positive), and _vice versa_. Then, the total of the column balances should always exactly cancel (“balancing the books”). For instance, the men pay $30 to the hotel. We would enter that transaction thusly: ```auto Men Hotel -30 +30 --- --- -30 +30 ``` The total of each column is shown below the line. The men paid $30, the hotel received $30, the totals add to zero. Next, the Hotel manager hands $5 to the bellhop to take back to the men. Let’s enter that transaction: ```auto Men Hotel Bellhop -30 +30 - 5 + 5 --- --- --- -30 +25 + 5 ``` The men have paid $30, the hotel has $25 and the bellhop has $5. Everything still balances. Finally, the bellhop give $3 back to the men: ```auto Men Hotel Bellhop -30 +30 - 5 + 5 + 3 - 3 --- --- --- -27 +25 + 2 ``` The men have paid $27. The hotel has received $25, and the bellhop has received $2. Together, received ($25+$2) equals paid ($27). The books balance. You’re trying to add a negative (paid) $27 to a positive (received) $2. Your first mistake is that the sum of negative 27 and positive 2 is _not_ 29, it is 25. Your second mistake is trying to balance this (incorrect) sum with the wrong thing (a 30 above the line, or a 30 that was below the line at some earlier point–I’m not sure which). kg m²/s² ---
**Author:** ![Newton\_meter](https://avatars.discourse-cdn.com/v4/letter/n/57b2e6/32.png) [@Newton\_meter](https://boards.straightdope.com/u/Newton_meter)\ **Post date:** [August 15, 2002, 2:59pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020/12 "2002-08-15T14:59:14Z")
> [@](#): > > \*Originally posted by Newton meter \* > **Your first mistake is that the sum of negative 27 and positive 2 is _not_ 29, it is 25.** Err, that ought to be negative 25, to be precise. ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [August 15, 2002, 3:19pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020/13 "2002-08-15T15:19:42Z")
Oh no! Not again! ---
**Author:** ![Keeve](https://avatars.discourse-cdn.com/v4/letter/k/f07891/32.png) [@Keeve](https://boards.straightdope.com/u/Keeve)\ **Post date:** [August 15, 2002, 4:10pm UTC](https://boards.straightdope.com/t/a-riddle-for-the-math-nerds/124020/14 "2002-08-15T16:10:19Z")
> [@](#): > > \*Originally posted by captainolev \* > \*\*They did each pay $9 there where three men and the bellhop did steal $2. That is why i posted it there is no logical explaniation on this answer. \*\* The answer given by Newton meter is correct but it is so long that I suspect non-mathgeeks can’t follow it. So I’m going to rephase it in very short non-geek terms: The mistake is that there is no reason to **add** the $2 **to** the $27, because what the bellhop did was to **subtract** the $2 **from** the $27, leaving $25 at the front desk. Really, think about it. It makes no sense to add $27 and $2 to get $29. What you want to do is to add $25 and $2 to get $27.