A train is travelling along, under the care of a driver, a guard and a ticket-collector.
Their names are Alan, Barbara and Colin, though not necessarily in that order.
On the train are three passengers, Ann, Bob and Cathy.

You are given the following bits of information.

1. Cathy lives in Norwich.

2. The guard lives in Cromer.

3. Bob cannot do algebra.

4. The passenger who shares their first initial with the guard lives in North Walsham.

5. The guard and one of the passengers, a good mathematician, are both poker players at the same local club.

6. Alan usually beats the ticket-collector at snap.

7. All three passengers live in different places.

Who does what, and where do the three passengers live?