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?

Very old problem! The way of telling the calculations was wrong. Each paid £9 totally £27, which also includes the bell boy pocketed. So bell boy's £2 should not be added with £27. Each paid £9 and have £1 on their hands.