Originally Posted by

**Mick** There are 32 people, so the 31 people asked must've shaken hands between 0 and 30 tîed. Everybody gave a different answer.

The person who didn't shake any hands must've come with the person who shook 31 hands.

The person who shook one hand must've come with the person who shook 29

Likewise 2 and 28

3 and 27, 4 and 26, 5 and 25, 6 and 24, 7 and 23, 8 and 22, 9 and 21, 10 and 20, 11 and 19, 12 and 18, 13 and 17, 14 and 16. That leaves the person who shook 15 hands as your room mate.