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Home » $ 2a + 4b = 6 $, - Anadea

$ 2a + 4b = 6 $, - Anadea

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 Now impose the even-sum condition.

📌 Sum is even if number of odd addends is even (since even + even = even, odd + odd = even).

📌 Prime numbers: 2 (even), 3, 5 (odd) → primes: one even (2), two odd

📌 Non-primes: 1 (odd), 4, 6 (even) → non-primes: one odd (1), two even (4,6)

📌 We need the total sum to be even, with exactly two prime rolls and two non-prime rolls.

📌 $ p \in \{2, 3, 5\} $: contributes parity: even if 2, odd otherwise

📌 $ np \in \{1, 4, 6\} $: contributes: odd (1), even (4,6)

📌 Let $ E $ = total number of odd numbers among the four rolls. We want $ E $ even.

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