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Home » Alternatively, each term mod 11: - jntua results

Alternatively, each term mod 11: - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 But instead, let’s use **generating functions with exclusion**, or a **reduced method**.

📌 Better idea: Use **inclusion-exclusion over the number of adjacent pairs**, but again, too broad.

📌 Instead, we use a **constructive endangered sequence method**:

📌 We attempt to **count valid sequences by placing high-frequency letters first with separation**, then fill with others.

📌 Let’s suppose we place the **C’s** with no two adjacent.

📌 To place 3 C’s with no two adjacent in 8 positions: we first place 3 C’s such that there is at least one space between them.

📌 The number of ways to choose 3 non-adjacent positions in 8 is a classic stars and bars adjustment.

📌 To place 3 non-consecutive positions: let the positions be $ x_1 < x_2 < x_3 $, with $ x_{i+1} \ge x_i + 2 $. Let $ y_i = x_i - (i-1) $, then $ y_1 < y_2 < y_3 $ in $ \{1,\dots,6\} $. So number is $ \binom{6}{3} = 20 $.

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