Ok here's another one. I found it on a math oddities website:
Three guys walk into an hotel and ask for a room with three beds. They just want to stay for one night. The man at the hotel tells them that the cost will be 30 dollars. They pay 10 dollars each and walk upstairs to their room. After some minutes the man knocks at their door, apologizing for a mistake. He made them pay the high season price and not the low season one, and since now it's the low season, he must give them 5 dollars back.
They are happy and appreciate the honesty of the man, so they tell him: "from these 5 dollars we will just take back 1 dollar each and we will give you the remaining 2 dollars as a tip for your honesty". The man thanks the guys and walks out.
Ok, they paid 10 dollars each (30 in total). They take back 1 dollar each (3 dollars in total). In this way they have paid 10-1=9 dollar each. So in total they have now paid 9*3=27 dollars. Plus the 2 dollars tip given to the man we get 27+2=29 dollars. Where is the missing dollar?
In reading this, my impression is that the dollar isn't really missing. Is it? I mean they gave 30, it was supposed to be 25, so they received 5 back. They kept 3 and gave 2.
Yet looking at that math it does look like 1 is missing.
Whew! This one threw me for a while. I knew, obviously, that the dollar really wasn't "missing", but I couldn't for the life of me explain why. I think I've figured it out, however. Here goes:
The amount that the hotel offers to refund is a red herring--that is, it's a completely misleading number. As Oniya referred to, the amount that actually matters is the total amount actually paid to the hotel (including the tip).
To illustrate, let's say our three fellows book rooms at the same hotel the next season. Once again, they pay the hotel $10 each, for a grand total of $30. This time, however, let's say that our hotel manager is so grateful for their business (and perhaps a little drunk) that he offers to refund $20. Once again, our generous travelers refuse, accepting only $1 back each and giving him the other $17 as a tip. So now our travelers have paid a grand total of $44 ($10 - 1 = 9 dollars each x 3 = $27 + the $17 tip = $44). Right?
Obviously that is not the case. In both examples, the travelers have paid $27 (10 initial - 1 back = $9 each x 3 = $27). The only difference is that, in the first example, the manager made a $2 (or $5 - 3) tip, while in the second he made $17 (or $20 - 3). The amount of the refund only factors into how much tip the manager gets, and has nothing to do with what the guys pay.