
Originally Posted by mgauss
OK here is one for you.
3 men go to a hotel and they are told the room is $ 30. They pay 10 each.
The manager then realizes that the room is only $ 25. So he gives the bellboy $5 and tells him to give it to the 3 men.
The bellboy pockets $2, as he figures three men cannot break a $5, and gives each man 1.
So the men paid each 101=9
which is 9*3= 27
and the bellboy kept 2
total $ 29. What happened to the $30?
Where is the dollar?
Ah, a classic! One of the problems in mixing math and the real world (or formal logic) is that math does not always recognize the fact that a new situation (or transaction) is taking place that is, in the real world, separate from the previous transaction and NOT connected to it mathamatically.
The one that freaks people out the most usually is the Boolean proof that it is mathamatically better  if you were on the old "Let's make a Deal" Show  to, if given the chance, switch your choice of doors after the first 'looser' door was reveiled. The math says, for example, if you picked Door #1 (out of three) and then Monty Hall showed you that door #3 had a skunk behind it and gave you the choice of staying with door #1 or switching to door #2, then  according to the math  you should switch, you will have a better chance of winning. The math is correct as far as it goes (VERY oversimplified...your first choice of door #1 was 1 in 3 of being the winning door, if you stick with that you still are stuck with your original 1/3 chance of having picked right but, if you change to door #2, that new choice is 1 in 2 so, better odds.). But it just doesnt sound RIGHT to people, even though you can show mathamatically that is actually the case. Somehow folks just KNOW after door #3 was taken out of the mix, is should be a 5050 chance no matter which door you have. A Math proffessor can "prove" you wrong, changing has a mathamatically better chance!
The problem is that the math does not recoginze the realworld logic/truth that, the very act of asking if you would like to change your choice actually CREATED a whole new choice, like it or not, that was 5050. It is as of Monty Hall said "haha, joke is on you, your first choice didnt count, you have to choose again, which door do you want." You are starting all over again you have no door choosen and you have a choice between door #1 and #2. Thus, it is really a totally new transaction that cancels out the original math.
With this problem the same thing happens. The original transaction was each guy giving the desk man a $10 bill. When the desk guy decided there was a mistake and money needed to be returned, a whole new transaction is created that, in the realworld, has no link mathamatically to the previous transaction.
This new transaction is: Clerk has $30 dollars, wants to give $5 to three guys. Guys get three, bellboy steals two. All adds up...when you look at it like that!


