 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-3/10e/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The all-zero amplitude is

2^{- n} \sum_{x} (- 1)^{f (x)} = 1 - 2 k / 2^{n}

, so its probability is

(1 - 2 k / 2^{n})^{2}

. For a general nontrivial

k

it lies strictly between zero and one.

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