The sequence 8, 11, 9, 1, 4, 6, 12, 10, 5, 7 contains 10 terms. Note t

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Module 2: Mathematical Induction & Counting Techniques.

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The sequence $8, 11, 9, 1, 4, 6, 12, 10, 5, 7$ contains 10 terms. Note that $10 = 3^2 + 1$ . There are four strictly increasing subsequences of length four, namely, $1, 4, 6, 12$ ; $1, 4, 6, 7$ ; $1, 4, 6, 10$ ; and $1, 4, 5, 7$ . There is also a strictly decreasing subsequence of length four, namely, $11, 9, 6, 5$ .

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