Bad mathematician

[Chido-Wan Kenobi]

3 guys who were traveling stopped at a motel for the night.
Each guy 1st spent $10, but took back $1 later. So in the end each spent $9. So 3x9=27. And the room service guy was tipped $2. So 27+2=29.
Hmmmm!!! $29 has been accounted for. So where is that remaining 1 dollar???

Math!!! Simple, but sometimes, complicated, or shall we say, Mind Boggling!!!

By Clifford AGA
I know it's wrong, but I can't see where it's wrong.

Yeah, this is an old one indeed, back from the days when Alexander wasn't "the Great", but just "the Pretty Good".

The trap you are falling into is assuming that the actual amounts paid by the "guys", plus the money stolen by the "room service guy" must equal 30. No, the only real money in the story is [$ the guys GOT BACK, which is $3], [$ in the concierge's pocket, which is $2] and [$ in the Hotel manager's hands, which is $25]. You will agree that the sum of these three amounts is $3 + $2 + $25 = $30, the original "real money". All the rest is just a play of words.

It will become clearer to you if you change the numbers a bit. For instance, say the room was actually worth $10/night, not $25. So, the manager would return $20 via the concierge, who, using the same logic as previously, might decide to pocket $8, and return $4 to each of the guests. Now you will see that, since in fact they paid only $6 each, 3 x $6 = $18, plus the $8 the concierge stole, gives you a total of $26. And now, you appear to be missing $4.

Worse, even. Say the room is actually $40/night. Now the concierge could go back to the guests, and demand an extra $6 from each - planning to bring $10 to the Manager and keep $8. Now, since they effectively paid $16 each, 3 x $16 = $48 + $8 in the concierge's pocket = a total of $56 ! The room was only $40 !! So you've CREATED $16 out of thin air !!! (Good business plan, I should say.)

So there...