# Riddle...Any takers? **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [November 22, 2000, 5:20am UTC](https://boards.straightdope.com/t/riddle-any-takers/42249 "2000-11-22T05:20:58Z")\ **Posts on this page:** 14\ **Page:** 1
**Author:** ![Just\_A\_Girl](https://avatars.discourse-cdn.com/v4/letter/j/5daacb/32.png) [@Just\_A\_Girl](https://boards.straightdope.com/u/Just_A_Girl)\ **Post date:** [November 22, 2000, 5:20am UTC](https://boards.straightdope.com/t/riddle-any-takers/42249/1 "2000-11-22T05:20:58Z")
Ok…my psychology teacher was kicking himself today because he couldn’t figure this riddle out. While the answer can be arrived at by logic, there’s not a definant answer but rather an explaination which is hard to simplify. (Well…for me anyway) Here it is: 3 men go to check into a hotel. The guy at the counter tells them that it will be $30 for one room. The men decide to share a room, and split the cost evenly; that is, each man pays $10. Later into the evening, the “behind-the-counter guy” discovers that the room was actually $25, not $30, and immediately sends a bellhop to the room with $5. The bellhop realizes it will be difficult to split $5 three ways so he pockets $2, and gives each man back $1. This means that each man has now paid $9 in his share of the room instead of $10. However, $9 multiplied by 3 is $27. Adding in the bellhop’s pocketed $2, that makes a total of $29. So where’d the other dollar go? While I know the basic idea of why this is so, I want to know if anyone has heard this riddle before and maybe has seen a simplified answer? Anyone else, give it a try! ---
**Author:** ![dpr](https://avatars.discourse-cdn.com/v4/letter/d/8797f3/32.png) [@dpr](https://boards.straightdope.com/u/dpr)\ **Post date:** [November 22, 2000, 5:23am UTC](https://boards.straightdope.com/t/riddle-any-takers/42249/2 "2000-11-22T05:23:55Z")
Oh god. Not again… This starts arguments around here. Just don’t ask about the three doors and the odds being 50-50 or 1 in 3 please… ---
**Author:** ![SPOOFE](https://avatars.discourse-cdn.com/v4/letter/s/c5a1d2/32.png) [@SPOOFE](https://boards.straightdope.com/u/SPOOFE)\ **Post date:** [November 22, 2000, 5:26am UTC](https://boards.straightdope.com/t/riddle-any-takers/42249/3 "2000-11-22T05:26:10Z")
[Homer Simpson] “It’s a ring toss.” [/Homer Simpson] (Hint: You don’t multiply the numbers at the end. 30-5=25. 25+3=28. 28+2=30) ---
**Author:** ![Sublight](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@Sublight](https://boards.straightdope.com/u/Sublight)\ **Post date:** [November 22, 2000, 5:26am UTC](https://boards.straightdope.com/t/riddle-any-takers/42249/4 "2000-11-22T05:26:30Z")
Try here: [http://www.straightdope.com/classics/a910621.html](http://www.straightdope.com/classics/a910621.html) –sublight. ---
**Author:** ![Danalan](https://avatars.discourse-cdn.com/v4/letter/d/76d3ee/32.png) [@Danalan](https://boards.straightdope.com/u/Danalan)\ **Post date:** [November 22, 2000, 5:26am UTC](https://boards.straightdope.com/t/riddle-any-takers/42249/5 "2000-11-22T05:26:46Z")
Haven’t you heard this one before? It is a fairly well-known example of false logic. The key is in the two additions, which should be separate. The men indeed paid $9 each for the room, for a total of $27. However, one should not add the bellboy’s $2 to that amount, but subtract the $2 from the $27 to get $25, the actual amount charged. ---
**Author:** ![Kat](https://avatars.discourse-cdn.com/v4/letter/k/b19c9b/32.png) [@Kat](https://boards.straightdope.com/u/Kat)\ **Post date:** [November 22, 2000, 5:27am UTC](https://boards.straightdope.com/t/riddle-any-takers/42249/6 "2000-11-22T05:27:13Z")
Simplified: Hotel keeps: $25 Bellboy keeps: $2 Man #1 keeps: $1 Man #2 keeps: $1 Man #3 keeps: $1 Total: $30 (25 + 2 + 1 + 1 + 1=30) The way the “riddle” is worded, you count the bellboy’s $2 twice and don’t count the three men’s $1 each ($3 total) at all. ---
**Author:** ![Just\_A\_Girl](https://avatars.discourse-cdn.com/v4/letter/j/5daacb/32.png) [@Just\_A\_Girl](https://boards.straightdope.com/u/Just_A_Girl)\ **Post date:** [November 22, 2000, 5:28am UTC](https://boards.straightdope.com/t/riddle-any-takers/42249/7 "2000-11-22T05:28:47Z")
I didn’t say anything about odds or doors! Seriously, I’m asking because I told my teacher I’d post it and see what people said. He was going nuts over this thing. I’m not trying to cause a problem…I’m just an innocent little girl! 😉 For dpr’s sake guys…don’t get all bent out of shape over it…I’m just curious! ---
**Author:** ![Just\_A\_Girl](https://avatars.discourse-cdn.com/v4/letter/j/5daacb/32.png) [@Just\_A\_Girl](https://boards.straightdope.com/u/Just_A_Girl)\ **Post date:** [November 22, 2000, 5:31am UTC](https://boards.straightdope.com/t/riddle-any-takers/42249/8 "2000-11-22T05:31:40Z")
> [@](#): > > \*Originally posted by Danalan \* > \*\*Haven’t you heard this one before? It is a fairly well-known example of false logic. > > The key is in the two additions, which should be separate. The men indeed paid $9 each for the room, for a total of $27. However, one should not add the bellboy’s $2 to that amount, but subtract the $2 from the $27 to get $25, the actual amount charged. \*\* awesome…that’s what I’m looking for. See, I figured out the whole adding thing and the “false wording.” But the nature of logic problems is to have a more simple explanation and that’s exactly it. Thanks a ton. 😃 ---
**Author:** ![Danalan](https://avatars.discourse-cdn.com/v4/letter/d/76d3ee/32.png) [@Danalan](https://boards.straightdope.com/u/Danalan)\ **Post date:** [November 22, 2000, 5:36am UTC](https://boards.straightdope.com/t/riddle-any-takers/42249/9 "2000-11-22T05:36:45Z")
Glad to help. (sigh of relief that I seem to have gotten it right, and so avoid the wrath of the collective SDMB) ---
**Author:** ![Mac\_Guffin](https://avatars.discourse-cdn.com/v4/letter/m/2bfe46/32.png) [@Mac\_Guffin](https://boards.straightdope.com/u/Mac_Guffin)\ **Post date:** [November 22, 2000, 7:17am UTC](https://boards.straightdope.com/t/riddle-any-takers/42249/10 "2000-11-22T07:17:43Z")
Back when I had to do math for a living, someone told me this riddle, and it took me almost a full day and night to figure it out. I came apon the answer in bed, at 4 am while staring at the ceiling going insane from it. Before I arived at the correct answer covered here, I also came up with this false answer. Later that same night, Two more guys check into the same motel, are told the room is $30 and decide to split it by paying $15 each. Later the “behind the counter guy” realizes that he made the mistake again, and calls the bellhop back with another $5 in $1 bills. the Bellhop, now overcome with greed from the earlier money, takes three dollars and gives each of the two guys a dollar each. so each man, having paid $14 times two, paid a total of $28 dollars, plus the three the bellhop kept makes $31. there’s yer extra dollar you lost earlier. I realize that the same false logic applies here, but that one almost made my brain leave my head for good. ---
**Author:** ![dpr](https://avatars.discourse-cdn.com/v4/letter/d/8797f3/32.png) [@dpr](https://boards.straightdope.com/u/dpr)\ **Post date:** [November 22, 2000, 7:45am UTC](https://boards.straightdope.com/t/riddle-any-takers/42249/11 "2000-11-22T07:45:01Z")
Sorry JaG, it’s just that some of the logic problems posted here have started wars (or at least minor revolutions). I was scared… nothing personal… ---
**Author:** ![Jack\_Batty](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jack_batty/32/3201_2.png) [@Jack\_Batty](https://boards.straightdope.com/u/Jack_Batty)\ **Post date:** [November 22, 2000, 4:38pm UTC](https://boards.straightdope.com/t/riddle-any-takers/42249/12 "2000-11-22T16:38:19Z")
Just A girl, you left out the most important part of the riddle. The name of the hotel is **The Gry Inn** , which in itself answers at least one other question. ---
**Author:** ![c\_goat](https://avatars.discourse-cdn.com/v4/letter/c/f4b2a3/32.png) [@c\_goat](https://boards.straightdope.com/u/c_goat)\ **Post date:** [November 22, 2000, 4:43pm UTC](https://boards.straightdope.com/t/riddle-any-takers/42249/13 "2000-11-22T16:43:01Z")
> [@](#): > > \*Originally posted by Just A Girl \* > **Ok…my psychology teacher was kicking himself today because he couldn’t figure this riddle out.** That’s pretty bad. I think the SD will never eradicate ignorance as long as this “riddle” keeps circulating. ---
**Author:** ![AWB](https://avatars.discourse-cdn.com/v4/letter/a/bb73d2/32.png) [@AWB](https://boards.straightdope.com/u/AWB)\ **Post date:** [November 22, 2000, 5:36pm UTC](https://boards.straightdope.com/t/riddle-any-takers/42249/14 "2000-11-22T17:36:21Z")
> [@](#): > > \*Originally posted by Just A Girl \* > \*\*Ok…my psychology teacher was kicking himself today because he couldn’t figure this riddle out. While the answer can be arrived at by logic, there’s not a definant answer but rather an explaination which is hard to simplify. (Well…for me anyway) Here it is: > > 3 men go to check into a hotel. The guy at the counter tells them that it will be $30 for one room. The men decide to share a room, and split the cost evenly; that is, each man pays $10. Later into the evening, the “behind-the-counter guy” discovers that the room was actually $25, not $30, and immediately sends a bellhop to the room with $5. The bellhop realizes it will be difficult to split $5 three ways so he pockets $2, and gives each man back $1. This means that each man has now paid $9 in his share of the room instead of $10. However, $9 multiplied by 3 is $27. Adding in the bellhop’s pocketed $2, that makes a total of $29. So where’d the other dollar go? > > While I know the basic idea of why this is so, I want to know if anyone has heard this riddle before and maybe has seen a simplified answer? Anyone else, give it a try! \*\* This is because he’s adding together the wrong dollars. The $27 that the guests paid for the room consists of the $25 that front counter has plus the $2 that the bellhop kept. To that, he’s re-adding the $2 that the bellhop kept. This doesn’t represent the total. Or algebraically: Divide the $30 into three parts: Let A = Final charge for room ($25) B = Amount that bellhop kept ($2) C = Amount refunded to men ($3) so A + B + C = 30 But the riddle is basically asking why: (A + B) + B \<\> 30 Of course it doesn’t, because it doesn’t include C and it double-includes B.