Bill Please!

Three people check into a hotel. They pay £30 to the manager and go to their room. The manager suddenly remembers that the room rate is £25 and gives £5 to the bellboy to return to the people. On the way to the room the bellboy reasons that £5 would be difficult to share among three people so he pockets £2 and gives £1 to each person. Now each person paid £10 and got back £1. So they paid £9 each, totalling £27. The bellboy has £2, totalling £29. Where is the missing £1?

A lightbulb idea?

Well, here's one that got me the other day...

This puzzle take place in two rooms. In the first room are three lightbulbs all connected to three switches in the other room. In this house a man is trying to figure out which switch activates which which bulb. Starting in the room with the switches I can tell you with certainty that this man can move from the switch room to the lightbulb room, not walk back in the switch room and still tell which switch activates which lightbulb, even with the constraint that the man has to move out of the doorway and into the lightbulb room to see the lightbulbs.
Your task is to tell me how.

Yeah it got me as well!

Nine Weights Problem and Twelve Weights Problem

These are old puzzles, certainly not my own (for once), but they are great thinking problems with really elegant solutions, see if you can solve them.

I have before me nine weights. Of which just one is slightly lighter. Using only scales I must find out which of these weights is this lighter one. How do I do this?

This problem is possible in just two weighs.

Slightly harder is the twelve weights problem...

I have before me twelve weights. Of which just one is slightly lighter. Using only scales I must find out which of these weights is this lighter one. How do I do this?

This problem is possible in just three weighs.