Eleven men for ten beds

From time to time, hoteliers write to me asking me organizational questions of this kind.

A hotelier had a sudden influx of guests. He arrived 11 at once asking each one a bed. The hotelier only had 10 beds, how did he accommodate them?

He put two in the same bed, but not before clarifying, that one of them would have a bed for him only as soon as he had placed the rest. Then he put the third in the second bed, the fourth in the third bed, and so on until the tenth, which he placed in the ninth bed. He still had an empty bed, which was occupied by man number eleven, and which had been temporarily placed on the first bed. How can it be?

As you can see, this riddle does not have a great mathematical difficulty. It is based on a paradoxical proposition. But it is so well hidden that it sometimes escapes us.

Solution

The trick is that the second man who places in the first bed also turns out to be also the eleventh which places in the tenth bed so it is really only locating ten people and that is why they all fit in 10 beds.