 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/3h/c/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

The ternary merges are

(.02, .03, .04) \mapsto .09

, then

(.04, .09, .14) \mapsto .27

, then

(.27, .28, .45) \mapsto 1

. One code is

x_{1} : 0, x_{2} : 1, x_{3} : 20, x_{4} : 21, x_{5} : 220, x_{6} : 221, x_{7} : 222.

Its expected length is

.45 + .28 + 2 (.14 + .04) + 3 (.04 + .03 + .02) = 1.36.

 New to topics? Read the docs here!