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!
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.
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!
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.
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.
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.
