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Home » The 10 Unforgettable SIMPSONS Episodes You NEED to Watch Before You Die! - High Altitude Science

The 10 Unforgettable SIMPSONS Episodes You NEED to Watch Before You Die! - High Altitude Science

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 N \equiv a + b + 3 \pmod{9}

📌 a + b + 3 \equiv 0 \pmod{9} \quad \Rightarrow \quad a + b \equiv 6 \pmod{9}

📌 So \( a + b = 6 \) or \( a + b = 15 \) (since \( a \geq 1 \), \( b \leq 9 \), maximum \( a + b = 9 + 9 = 18 \), but we'll check both).

📌 First, count solutions to \( a + b = 6 \), \( a \geq 1 \), \( b \geq 0 \):

📌 \( a \) ranges from 1 to 6 → \( b = 6 - a \geq 0 \), so 6 solutions.

📌 Now, \( a + b = 15 \):

📌 \( a \geq 6 \) (since \( b \leq 9 \)), and \( a \leq 9 \). So \( a = 6,7,8,9 \):

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