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308 versus 7mm 08 - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Among four consecutive odd integers, one is divisible by 3. If one is divisible by 9, we get $3^2$, and if another is divisible by 3 (which happens in most cases), but since the step is 2, two of them can be divisible by 3 only if spaced by 6 — but only one in every three odd numbers is divisible by 3. So only one multiple of 3. So $3^1$ is guaranteed, $3^2$ is possible, but not guaranteed.

📌 Wait: recurring pattern — in any four consecutive odd numbers, the residues mod 3 cycle. Since step is 2, and $2 \cdot 3 \equiv 0$, but over four steps, one must hit 0 mod 3. So exactly one multiple of 3 per such quartet.

📌 But is that multiple divisible by $9$? Not always — e.g., $n = 3$: 3 (div by 3 but not 9), $n = 9$: 9 (div by 9), $n = 15$: 15 (not div by 9). So only guaranteed $3^1$.

📌 Similarly, for $5$, not always.

📌 Now check if divisible by $9$: yes, as shown above.

📌 Check for $3 \cdot 9 = 9$: yes.

📌 But what about $3 \cdot 5 = 15$? We saw $120$ in previous problem, but here product $1 \cdot 3 \cdot 5 \cdot 7 = 105$, divisible by $15$, but $3 \cdot 5 = 15$ — yes. But $3 \cdot 3 = 9$: $105$ not divisible by $9$. So $9$ does not always divide $P$.

📌 So far, guaranteed divisors: $3$. But is $3 \cdot 3 = 9$ always? No.

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