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        riddles >> hard >> 3 Men and a Hotel Room
        
(Message started by: macdaddy on Jun 5^th, 2006, 7:27pm)

Title: 3 Men and a Hotel Room
Post by macdaddy on Jun 5^th, 2006, 7:27pm

i can pretty much get any riddle with time but after an hour i still cant get this someone please explain it.

Three men go to a cheap motel, and the desk clerk charges them a sum of $30.00 for the night. The three of them split the cost ten dollars each. Later the manager comes over and tells the desk clerk that he overcharged the men, since the actual cost should have been $25.00. The manager gives the bellboy $5.00 and tells him to give it to the men. The bellboy, however, decides to cheat the men and pockets $2.00, giving each of the men only one dollar.
Now each man has paid $9.00 to stay for the night, and 3 x $9.00 = $27.00. The bellboy has pocketed $2.00. But $27.00 + $2.00 = $29.00. Where is the missing $1.00? WTF?

Title: Re: HELP! hotel stay
Post by Weazel on Jun 5^th, 2006, 7:46pm

[hide]The two dollars is included in the $27. It should be $27 - $2 + $5 = $30.[/hide]

Also, you can search the forums for the answers, and this riddle should be in the easy section.

Title: Re: HELP! hotel stay
Post by Icarus on Jun 6^th, 2006, 3:24pm

While I agree that this riddle deserves to be in the easy section (there is no deep truth behind it - it just misleads the reader), William placed it in the Hard section on the Riddles page, so here is the appropriate forum for it. You will find several earlier threads for it though, if you look.

As Weazel has said, the two dollars the bellboy took came from the $27 the men paid, so it should not be added to that $27 again. The correct accounting is:

$25 (hotel) + $2 (bellboy) + $3 (men) = $30.

Title: Re: HELP! hotel stay
Post by checker on Nov 26^th, 2006, 11:05pm

on 06/06/06 at 15:24:20, Icarus wrote:

the two dollars the bellboy took came from the $27 the men paid, so it should not be added to that $27 again. The correct accounting is:

could you please explain this more properly!

Title: Re: 3 Men and a Hotel Room
Post by rmsgrey on Nov 27^th, 2006, 5:58am

Of the $30 originally put into the till, look at where each dollar ends up. $25 stays in the till, $2 goes to the bellboy, and $3 to the customers ($1 each)

A more accurate way to phrase it would be "Each man has paid $9 to stay for the night (3 * $9 = $27). The bellboy has pocketed $2 and $27 - $2 = $25 which is what's left in the motel coffers."

Title: Re: 3 Men and a Hotel Room
Post by jollytall on Nov 27^th, 2006, 12:52pm

But solve this:

There were about 25 threads on this topic. Now we opened one more. That should be 26. Then everybody recognises that probably even 25 was at least 24 more than should be. Still we keep two threads active in the hard and medium sections.
So the question: Why don't we open a 27th in the easy section and keep all the three on the top of the lists. That would make 30 (27 in total + the 3 active).

Title: Re: 3 Men and a Hotel Room
Post by Sameer on Nov 27^th, 2006, 1:25pm

Wow, i can't put these feelings in words.. we are discussing same problem in two different threads active at the same time but different currencies ;). Btw, jollytall's and my posts are two similar posts, where did the third similar post go? ;D

http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1164608432

Title: Re: HELP! hotel stay
Post by Icarus on Nov 27^th, 2006, 4:49pm

on 11/26/06 at 23:05:47, checker wrote:

could you please explain this more properly!

I don't know how I could possibly explain it more clearly! The incorrect accounting adds the bellboy's $2 to the $27 that the men paid to get $29. But in fact, those $2 were two of the 27 dollars. Adding them to the 27 dollars is counting them twice (while ignoring the returned $3, which is why it comes short of $30).

Title: Re: 3 Men and a Hotel Room
Post by BNC on Nov 28^th, 2006, 3:11am

Maybe these variants will help:

1) The manager tells the bellboys to return the whole $30, as these are his guests. The bellboy pockets all $30, returning nothing.
Now, they paid 3X10=$30. The bellboy has $30. But 30+30=60, not 30... where did the extra $30 come from?

2) same as before, but the bellboy is honest, and returns the money.
They paid 3X0=$0, + $0 at the belboys = $). Now there are $30 missing!!!!

Title: Re: 3 Men and a Hotel Room
Post by Icarus on Nov 28^th, 2006, 4:42pm

Lets try this: each . is a dollar:

(1) Men give the money to the bellboy:

  man 1  |  man 2  |  man 3
..............................

(2) Bellboy gives $25 dollars to the manager, keeps $5

  Manager                Bellboy
..............................

(3) Bellboy gives $3 back to men

  Manager           Bellboy Men
..............................
|<--------- 27 ---------->|

(4) the accounting that comes up with $29:


.............................
|<--------- 27 ---------->|

Note that $29 is reached by adding the bellboy's $2 to the $27 dollars, even though they are already accounted in those $27. This is why there are 4 blue points in the last row, even though the bellboy only gets $2.

Does it make sense now?