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## The Extra Dollar in the Hotel

Logic puzzles require you to think. You will have to be logical in your reasoning.

 Puzzle ID: #110 Fun: (2.74) Difficulty: (2.05) Category: Logic Submitted By: giraffe Corrected By: Winner4600

Three people check into a hotel. They pay \$30 to the manager and go to their room. The manager finds out that the room rate is \$25 and gives \$5 to the bellboy to return. On the way to the room, the bellboy reasons that \$5 would be difficult to share among three people, so he pockets \$2 and gives \$1 to each person. Now, each person paid \$10 and got back \$1. So they paid \$9 each, totalling \$27. The bellboy has \$2, totalling \$29. Where is the remaining dollar?

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## Comments

 captbob61 Mar 27, 2002 An old riddle, but a good one. Jasin Jul 11, 2002 good one shop-a-holic Sep 02, 2002 cool SPRITEBABE44 Dec 29, 2002 g8t teaser old but i cudnt reember the answer until now thanxs lol z-man Feb 19, 2003 Could someone explain WHY you can`t do the math 27 + 2, other than because it doesn`t work... WHY doesn`t it work??? jimbo Apr 05, 2003 It's a cash flow thingie. You look at who paid out what and where it went. The men paid \$30 out but got \$3 back so they really only paid out \$27. Now where did the \$27 go? \$25 went to the manager and \$2 to the bell-hop. Jason1385 Apr 06, 2003 I understand the "cash flow" analysis, but it doesn't answer why, mathematically, it's wrong to calculate the problem as presented. I seem to recall something about the problem, as stated, mixes the associative and distributive properties, which is improper, but I don't really understand what that means and why. Does anyone else know? jbarbie23 May 18, 2003 I can field this one - the \$27 + \$2 math doesn't work because the \$2 is PART OF the \$27 they paid (\$25 to the hotel, and \$2 to the bellhop). "They each paid \$27, plus the \$2 for the bellhop..." - well, that counts the \$2 twice now, and doesn't count the money in the guests' pockets. The riddle leads you to try to add part of the payment to the total payment, instead of adding what was paid to what was not paid. That's why it doesn't work; it has nothing whatever to do with associative or distributive anything! Smithy Aug 08, 2003 Classic cnmne Jan 22, 2004 This is a classic case of misdirection. You are given a scenario with a bunch of numbers. You are then given a series of statements that use those numbers, and are intentionally misdirected to add the bellboy's \$2 to \$27, thus creating the missing dollar. Not realizing that you have been tricked, you spend the rest of your life wondering where the dollar went. coolbrain2291 Jan 23, 2004 old but nicely put nice teaser ryanb_11 Jan 28, 2004 The answer it gives seems a little confusing to me. I look at it like this: In the end they paid \$25 for the room, the Bellboy has \$2 and each person has \$1 dollaer, 1+1+1=3. Thus the \$30 is accounted for!! Just my way of looking at it anyway. bbbz Mar 29, 2004 ok you understand the cash flow thingie, but you want to know why you cant just add 27 and 2 as stated in the problem. Most simply put your adding when you should be subtracting. the two dollars should be subtracted from the 27 to give you 25, the actual rate for the room. kreed Jun 22, 2004 Classic 1 but I still don't get it. beijing200820 Jun 23, 2004 It confused me but I got it. Pretty funny! Eriegurl Dec 31, 2004 I think I have a different answer. When the guys pay the 30 dollars, the lady realizes they only should have paid 27 dollars, so she take out an extra 5 dollars, which makes the total 35 dollars, gives it to the bell hop, he pays the guys each a dollar... and ends up with 32 since he's giving money back... and keeps the last 2 dollars... which would be taking money away as a tip, so theres the last 2 dollars subtracted to get to 30 dollars. Am I a genuis or what? Just kidding... but it makes sense if you understood that. It kinda makes sense. Atropus Jan 31, 2005 Cool teaser I guess you are deliberately misdirected from figuring the money that the manager has into the equasion... either way it's mathematics like that that have lead to me losing SO MUCH MONEY over the last couple of years. I need to keep a better eye on my budget freezequeen Mar 24, 2005 Wow,that was good!!!I think ive haerd it before.But not on this website. darthforman Apr 20, 2005 That was a nice one. You really had me thinking there. bigSWAFF_69_ Jun 07, 2005 why does the bellhop get \$2? good teaser tho joeyleahs2 Sep 14, 2005 i am a 6 grader and they gave me this exact one. what is the longest time it took to find this out ElaineSokolowsk Oct 31, 2005 Actually, by definition, the answer to this question is wrong. The answer to this question deals with the mediumof money. Money only uses two decimal places. In order to account for the full extra dollar, one must calculate the division of the dollars, observe the decimals, and NOT round. This way, the full value of the missing dollar is represented. It has to do with theoretical math and imaginary numbers. But technically, this is impossible... because you need all... eh... twelve decimal places to make up for the missing dollar. Elaine PS- My college Calc class worked this problem out today using the imaginary numbers theorum. bagogirl Nov 06, 2005 yes, the question was where was the extra dollar, not how to figure out-well, i don't exactly get what answer is being answered pinkyjr Dec 21, 2005 huh? ncsu_gurl_2011 Jan 27, 2006 i'm not good with numbers... SPUTNIK2 Jan 27, 2006 My dad has been telling this one for years....and I still don't get it! (user deleted) Feb 02, 2006 This was a great teaser. Thumbs up. I had to really think about it. I emailed it to my mother, and she drove me crazy trying to figure it out. teen_wiz Feb 09, 2006 WOW . I'm confused. Too hard for me. Great one though! vancon Feb 11, 2006 It is an oldie but still clever and very fun. Thanks for the teaser! MadDog72 Mar 12, 2006 The problem may be hard and confusing but it has a simple answer. No theoretical math is required, certainly not imaginary numbers. I have no idea how this problem could have anything to do with imaginary numbers or calculus. zakp Mar 18, 2006 Great redraptor50 Mar 18, 2006 Great teaser, keep these coming. mitzimesser Mar 25, 2006 Awesome teaser. It never struck my mind that the bellboy's 2 dollars counted toward the cost of the room & must be added to the amount that the manager was holding. Very nice. jntrcs Apr 12, 2006 intresting this guy ended up telling this at a camp i went to but got the answer all messed up and said it was a mathmatical error so i asked my dad and he explained it to me like this. awesome spazzyjazzy93 May 13, 2006 wow that made my brain hurt! great teaser! fem81uk May 19, 2006 good one, i worked it out babygirl8195 Jun 01, 2006 my grandpa tought me this when i was really little. i got it right! (user deleted) Jun 05, 2006 so where is the extra dollar actually then? i understand how to figure out the details, but wheres the extra dollar? how would u answer that? Unraveled Jun 07, 2006 hotrodmeg - there was no extra dollar. The men paid 30 dollars and got 3 back. The manager recieved 30 dollars, but paid 5 back. The bellboy got 2 dollars. The men are at -27 and the manager is at +25 and the bellboy is at +2. The 27\$ that was paid is still present. Make sense? cyberstar5150 Jun 29, 2006 Wow. I'm usually good at math, but I got stumped schatzy228 Jul 11, 2006 WOW , 4 YEARS LATER, IT IS STILL CONFUSING PEOPLE THE SIGN OF A TRUE CLASSIC blagh Aug 08, 2006 \$30 a hotel room! Where's that at? It's cheaper then the rent at my house! vinchenzo Aug 22, 2006 to answer this, you would divide the total of the room, \$25, by three. therefore each man originally paid \$8.33 for the room. add the extra dollar they got back and the real total per man is \$9.33, not \$9 each as the question states. times that by three is \$27.99, plus \$2 is \$29.99. so where did the extra penny go? Battery Aug 30, 2006 the following day two men go and stay at the same hotel and pay \$30 and go off to their room. the manager forgot again that it was only \$25 and gave the bellboy \$5 to give to them. the bellboy this time keeps \$3 for himself and gives \$2 back to the men. take tha away from the \$30 they originally paind makes \$28 plus the bellboy's \$3 equalling \$31! There's your missing dollar! rrn0rrnrrnY Sep 03, 2006 lol@Battery I think this was a good teaser. It is in the trick category so it is meant to attempt to get you thinking in the wrong direction. No calculus or imaginary numbers, maybe heard before, but still what a trick teaser should be. 2rubystar2 Oct 13, 2006 I like the way you explained it. I never actually understood that riddle before but now I do. Thanks! eamon Nov 01, 2006 A classic example of a "nonsense" sum. Just because one can make a statement that such and such equals something, does not make it true. It has to make sense at each step along the way and in the entirety. The hotel has \$25. The bellboy has \$2 and each of three guests have\$1. 25+2+1+1+1=30. Nothing is missing. In fact, they "paid" \$27 for the room -- \$2 to the dishonest bellboy and \$25 to the manager. Adding the \$2 to this \$27 AGAIN is just nonsense -- so of course it produces a meaningless total of \$29. To the folks who still had trouble understanding... the trick is really about the language of the problem and NOT the arithmetic. (user deleted) Dec 18, 2006 I heard this riddle when I was living in Germany but the man didn't know the answer. That was 6 years ago and I continued to ask people this riddle to try to get the answer but to no avail...I'm glad I finally have the answer I can now let my husband know too because we were both stumped! SPUTNIK2 Feb 08, 2007 same here, my daddy has told this story, but he doesn't say anything about the bellhop having 2 dollars King_of_Smart Aug 07, 2007 Very tricky teaser, but still VERY FUN!!! princesspt Sep 28, 2007 i honestly DONT GET IT. dogg6pound9 Jan 09, 2008 i'm 32 years old and i first heard this when i was in 5th grade (does that tell you something?)... simply put, there is no missing dollar... it's called ORDER OF OPERATIONS... you cannot take an addition/substraction equation and turn it into a multiplication equation... \$30(original payment) - \$5(refund)=\$25(actual payment) they did not pay \$27 for the room, they paid \$25... it's not their fault the bellhop ripped them off \$2 (\$25 + \$2=\$27) and only gave them each \$1 back (\$27+\$1+\$1+\$1=\$30, the original payment) anymore questions??? dogg6pound9 Jan 16, 2008 here' something i thought of last nite... if the bellhop is as much a thief so as to take \$2, then he should just stick all \$5 in his pocket and not say anything to anyone... problem solved shawneeo Apr 15, 2008 Yeah, it's just the way it's worded, but it's worded so well that you just don't notice at all... They get back the dollar each, and then they would say "We each now have paid 9\$ making a total of \$27." Right, \$27 is how much they believe they paid for the room now, because they got a dollar back each from the bellboy. The manager has \$25, and the bellboy still has \$2, which makes the \$27 they think they paid. They first each gave ten making it a total of thirty. Then they each got back a dollar, making the total they paid 27. The bellboy has two, so the total money is now not 30, but 27. the manager has 25 and the bellboy has 2. The trick is that the thirty, changes when they each get back the dollar! So the total is no longer 30. It was only 30 until they each got the dollar back. I'm not gonna think about this anymore, that's it! Wow, that is one tricky teaser! brain23 Apr 20, 2008 The title is a mistake. It should say "The Missing Dollar in the Hotel." (user deleted) Aug 07, 2008 The \$1 was lost in the maths. Like people said the bellboys \$2 should have been subtracted from the \$27 not added, as that is double counting it as the bellboys \$2 is already included in the \$27. But To answer the actual question of 'Where is the "missing" dollar?' The difference is between the \$3 returned and the \$2 the bellboy has. \$3 - \$2 = \$1. e.g. Change the question to the room rate was \$26, the manager returns \$4 but the bellboy keeps \$1. Then you have 3 x \$9 = \$27. The bellboy has \$1, so \$28. Where are the missing \$2 dollars? Answer: the difference between the \$3 returned and the \$1 the bellboy has. \$3 - \$1 = \$2. e.g.2. The room rate was \$24 dollars. Manager returns \$6. Bellboy keeps \$3 (because he's a thief!) and returns \$3. 3 x \$9 = \$27. Add the \$3 with the bellboy = \$30. Here there is no missing \$ because there is no difference between the amount the bellboy kept and the amount he returned. coolboy66 Jul 02, 2011 So, the three men payed \$30, \$10 each. The room only costed \$30. The manager gave the bellhop \$5 to return to the men. The bellhop thought it was difficult to share \$5 between 3 people and gave them \$3, keeping \$2. Now, the three men payed \$10 each, getting \$1 each back. So they payed 3x\$9, or \$27. Now the bellhop has \$2, making the total \$29. Adding the \$3 they got back, it equals \$32. Where did the extra \$2 come from?

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