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How did William Tutte determine that the Tunny machine used 12 wheels?

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The Colossus computer at Bletchley Park, Buckinghamshire, England, c. 1943. — Colossus Funding for this code-breaking machine came from the Ultra project.

In January 1942, British code breaker William Tutte analyzed intercepted German transmissions and successfully identified systematic patterns within the messages. By studying these patterns, he deduced that the "key"—the masking letters used to encrypt the original German text—was generated by a system of 12 different wheels inside the Tunny machine.1