Level 3, Propeller head

Grover's search

Four answers start with equal chances, one each in four. One round leaves the marked answer, drawn here as 11, certain, and the other three empty.

Grover’s search is the adding and the cancelling done at a larger size, published by Lov Grover in 1996. A marked answer grows and the others shrink, so the final measurement is more likely to show the marked one. The rounds grow with the square root of the number of candidates, where a classical search grows with the number itself.

On four candidates the arithmetic fits on one sheet, and one round leaves the marked answer certain. Keith’s poster still says the machine tries every answer at once, while the sheet shows one bar growing and three bars shrinking.

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