 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/12/c/i/solution

The two possible colour orders are

GGRR

and

RRGG

. Thus the answer is

2 .

They correspond to the positive and negative four-step excursions with first return time four.

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