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Alternative Solution

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?

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