Label the vaults 1 to 4 from left to right.

Let {x(1), x(2), x(3), x(4).....} be a strategy i.e. the person (Mina or the Vampire) will be at vault x(i) on day i

Mina's strategy - {3, 3, 2 , 2, 3}

Vampire's Possible Strategies:

1. {1,2,1,2} - caught on 4th Day
2. {1,2,3,2} - caught on 4th Day
3. {1,2,3,4,3} - caught on 5th Day
4. {2,1,2} - caught on 3rd Day
5. {2,3} - caught on 2nd Day
6. {3} - caught on 1st Day
7. {4, 3} - caught on 2nd Day

No matter where the Vampire starts, he will be caught.

Did I miss anything?