The Bellhop Problem

[Edwardo Piet]

I suck at maths but I love mathematical problems that require more logic than numeral calculation.

A classic one is The Monty Hall problem. Another is 0.9...=1

Both of those have been covered on AF.

But as far as I am aware The Bellhop Problem hasn't been covered.

It's an interesting problem with a clever solution. And for those who are unfamilar with it... enjoy:

You present the problem and it's solution. What is the question?

ETA: Do you want the math or the logic? I can go either way.

No I just find it interesting to talk about. I can see how the solution makes sense but it's hard for me to figure out why people make the mistake initially and if I look at it from the perspective of the problem it's easy to get lost in it again. The explanation at the end about how the $3 is already included... is clear but escapes me. If I count the money the guests keep first and then the money to the Bellhop... I appear to make the mistake. But if I instead give the money to the Bellhop first, and then I remember the guests are still holding $3... I don't seem to make the mistake then.

I grasp the solution just as easily as I do the problem to The Monty Hall problem... it's just harder to see the problem more clearly on this one. And why it happens.

The reason why I made this thread is because when the interesting Monty Hall problem and 0.9...=1 thing was demonstrated elsewhere... there were a lot of incredulous people who simply could not believe the solutions. And then an interesting discussion would happen as people who understood the solution explained to the people who didn't understand it... and the people who didn't understand it kept doubling down because it was so counterintutive.

Funny really, because I think this problem is much more difficult than The Monty Hall Problem... but I guess that one is more counterintutiive for most people. I find neither counterintutiive and both solutions to be clear... but with The Monty Hall Problem I am no longer able to even perceive the problem anymore.... the solution is always there staring me in the face. But with this problem I only see the solution when I look at it from the perspective of the solution... as soon as I try and use the faulty reasoning of the problem I end up left over with $1 again and can't see what I did wrong. All I know is that when I follow the solution it all works out correctly. Does that make sense?

---

Oops, a nice presentation of the problem if you'd cut it down to just part on the left side of the board.

It seems most people don't like spoilers as much as I do!