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Home » Is 37 â¤ 39 and prime? Yes. - Dachbleche24

Is 37 â¤ 39 and prime? Yes. - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 So \(a_5 = 13\)

📌 But this counts **classifications** — each position gets H or S, no two adjacent H’s.

📌 Since the substations are in a fixed line (distinct positions), and each is assigned one mode, the total number is exactly the number of such binary strings: 13.

📌 Wait — but earlier we computed \(\binom{n-k+1}{k} = \binom{5-4+1}{4} = \binom{2}{4} = 0\) — invalid.

📌 Mistake: formula \(\binom{n-k+1}{k}\) is for placing \(k\) non-adjacent indistinct items? No — standard formula for number of binary strings of length \(n\) with no two consecutive 1’s is \(F_{n+2}\), where \(F_1=1, F_2=1, F_3=2, F_4=3, F_5=5, F_6=8, F_7=13, F_8=21\)

📌 So \(F_{5+2} = F_7 = 13\) — matches.

📌 Thus, number of valid assignments is 13.

📌 But wait — no: \(F_{n+2}\) gives the count for \(k=1\) to \(k=\lfloor (n+1)/2 \rfloor\), but we want **exactly 4 H’s**? No — the problem does not fix number of H’s. It allows any number, as long as no two are adjacent.

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