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bethel woods center for the arts upcoming events - Coaching Toolbox

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 $S(3,3) = 1$

📌 $S(4,2) = 2 \cdot S(3,2) + S(3,1) = 2 \cdot 3 + 1 = 7$

📌 $S(4,3) = 3 \cdot S(3,3) + S(3,2) = 3 \cdot 1 + 3 = 6$

📌 $S(5,3) = 3 \cdot S(4,3) + S(4,2) = 3 \cdot 6 + 7 = 18 + 7 = 25$

📌 Thus, $S(5,3) = 25$

📌 Since the panels are indistinguishable, no further labeling is needed. Therefore, the number of ways is $\boxed{25}$.

📌 Question: A climatologist records daily rainfall anomalies over a 7-day period, each day’s anomaly being an integer from $0$ to $4$ mm, inclusive. How many sequences of anomalies are possible such that no two adjacent days have the same anomaly?

📌 Solution: Each day has $5$ possible values: $0, 1, 2, 3, 4$.

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