What happened to that dollar in the hotel problem?
Nothing. Each guy paid $9. So $27 altogether. The hotel kept $25, the bellman kept $2.
The key is that the bellman’s $2 is part of the $27 total. So it makes no sense to add $27 + $2.
I remember my best friend in fifth grade, Matt, posing this problem to me as a “hole in mathematics”. He was a wonderful story teller and it made the puzzle very compelling. It’s a lovely one. But it’s not a hole in mathematics.