Sure success partial search
  Partial search has been proposed recently for finding the target block containing a target element with fewer queries than the full Grover search algorithm which can locate the target precisely. Since such partial searches will likely be used as subroutines for larger algorithms their success rate is important. We propose a partial search algorithm which achieves success with unit probability. 
Byung-Soo Choi, Thomas A. Walker, Samuel L. Braunstein