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Roccotab  (Level: 60.4 - Posts: 185)
Tue, 1st May '07 8:33 AM


Ok my brainstorming friends help me out. I know someone has the answer.

If 3 people go to a hotel in Philly, and find a room for 30 bucks (good luck), and they split the expense 10 bucks each. They get to their room, and the Inn keeper decides they are a pretty cool bunch, and decides 30 bucks was a bit steep (again good luck) so he decides to give them a discount and sends the bell hop to their room with 5 bucks, and tells him to return it to those nice folk (right). Anyway the bell hop decides hey I ain't giving them all this I think I will just give them a buck each, and keep 2 for myself (probably true).

With the bell hop returning 1 buck each to them now they have only paid 9 bucks each for the room instead of 10 correct? Are you still with me? So lets do the math, if they only gave 9 bucks each for the room 9x3=27, and the bell boy kept 2 bucks for hisself 27+2=29 what happened to the other dollar from the original 30 they paid.

Perplexed Rocco.

Gypsylady  (Level: 148.2 - Posts: 6097)
Tue, 1st May '07 8:51 AM

30-2 (for the bell hop) means 28.00 to be divided among the (3) which equals 9.33333333333333333333 which can't be divided moneywise, so I think one of the 3 got cheated.


Roccotab  (Level: 60.4 - Posts: 185)
Tue, 1st May '07 9:31 AM

My problem is not that the money is missing I guess because it is still there, but why doesn't the simple reverse math in this equation add up the same both ways? I wonder if it were a million dollars, and 3 contractors gave me 10 mil each, I realized the material was cheaper, and gave them back 1 mil each, then paid another guy 2 mil for something else, when the ceo,s did the math that way they might wonder what i did with the extra mill lol.

Gypsylady  (Level: 148.2 - Posts: 6097)
Tue, 1st May '07 9:35 AM

It's getting too deep for me, Rocco!


Garrybl  (Level: 291.5 - Posts: 6770)
Tue, 1st May '07 9:43 AM

This is a great puzzle. I remember being impressed by the misdirection when i first met it. Consider the 30 dollars they give the innkeeper.

The Innkeeper gets 25 of those dollars, they get three back and the bellboy gets two. that adds up to 30.

Conversely the room cost 25 dollars; they paid 27 dollars, and 25 of that goes to the innkeeper 2 to the bellboy.

the room did NOT cost 30 dollars. Change 30 to 3000 to make the numbers look more implausible and have the gap become clearer.


Texlewee  (Level: 34.1 - Posts: 601)
Tue, 1st May '07 9:46 AM

10 X 3 = 30 ( Amount they originally paid) Subtract 5 = 25 (Amount after refund)
Add 2 (Amount bellhop kept)= 27 27/3 =9

Here's the fallacy: The #30 should not be the primary focus.You have to go with the actual dollars spent and adjust from there.

Assume 30 = original dollars spent. Actual refund amount = 3 dollars. 30-3=27. The "5" is irrelevant.

The problem with the math in the example is that it credits the 2 dollars against amount paid. They didn't pay the bellhop an amount ABOVE the 27 dollars. He KEPT the amount that equaled the difference between 25 and 27. 2 dollars was the difference. NOT an additional fee on top of rent paid. Using the math that asks "where's the extra buck" implies that the 2 dollars was given as extra AFTER the refund.

To add the 2 dollars back into the total amount paid implies that the original debt was 32 dollars instead of 30.

Donden  (Level: 112.5 - Posts: 2127)
Tue, 1st May '07 9:54 AM


Roccotab  (Level: 60.4 - Posts: 185)
Tue, 1st May '07 9:59 AM

But the hotel guests actually paid 27 dollars. Originally they paid 10 each, and each recieved a 1 dollar refund so the fact still remains the guests paid 27.00 9 each for their room.

Smeans  (Level: 109.2 - Posts: 301)
Tue, 1st May '07 10:04 AM

total cost of the hotel room $30 orignally

After a refund $25
each person paid roughly $8.34 or $8.33

Each person got $1.00 back even though they should have gotten $1.66 or $1.67

If you have the total of the reduced room. $25 plus the $3 that the people got back it knocks it up to $28....then add in the $2 the bell hop skimmed off the top. You get your $30

Roccotab  (Level: 60.4 - Posts: 185)
Tue, 1st May '07 10:16 AM

I knew there were some of the smartest people on the planet here on sploofus Island lol. I guess as long as the bottom line adds up, and the cash drawer matches the reciepts for the day all is well. At least if I am the Inn keeper I can sleep soundly knowing all is right with the audit lol.

Suzer22  (Level: 165.6 - Posts: 1982)
Tue, 1st May '07 10:22 AM

All may be right with your bottom line, but you'd better fire that bellboy!

Roccotab  (Level: 60.4 - Posts: 185)
Tue, 1st May '07 10:28 AM

LOL Suzer I would, but he's my brothers dad lol.

Smeans  (Level: 109.2 - Posts: 301)
Tue, 1st May '07 10:41 AM

The people have the illusion that they paid $9.00 each for the room. When in fact truth be told they didn't. They all think....great we each got a dollar back and think that the room rate had been cut to $27.00 for the night. When in fact it had been cut too $25 and the bell hop kept the extra $2 for himself leaving the room cost at $25. And yeah they better find a new bell hop. LOL

Berylm  (Level: 162.4 - Posts: 478)
Tue, 1st May '07 12:41 PM

Forget the $30.

Cost of room = $25
Bellhop's take = $2
3 people paid = $27

$27/3 = $9 each.

Baggiob  (Level: 143.2 - Posts: 888)
Tue, 1st May '07 12:47 PM

That is one of these questions that crops up quite a lot (although I have not heard it asked for a few years now) it is all about how you look at they question.

Most people presume that each person has paid $9 and the bell boy has taken two, which adds up to 29, but one has to remember, and spin it on its head, and say that the room shoudl have cost $30 but was reduced to $25, so as others have said, the 3 people paying for the room have actually lost out on some money.

Good question by the way.

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