 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ia/paper-2/1e/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

A transposition exchanges exactly two letters and fixes the rest. A permutation cycle

(a_{1} a_{2} \dots, a_{k})

sends each displayed letter to the next, sends

a_{k}

a_{1}

, and fixes all other letters.

After imposing

σ (1) = 2

, the remaining

n - 1

domain elements may be sent bijectively to the remaining

n - 1

values in arbitrary order. Hence the number is

(n - 1)! .

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