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Let's call the vaults as A,B,C,D
assuming you cannot return back to A from D
Day 1, check vault B, the vampire must be in A,C,D
Day 2, check B again, the vampire must be in D, since if it was in A it must go to B, if it was in C it can only go to B or D.
Day 3, check C, and KILL.
IF you can return from DA, but not AD
Day 1, check B, the vampire must be in A,C,D
Day 2, check B again, the vampire must be in D.
Day 3, check C, the vampire must be in A
Day 4, check B, and KILL. :P