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Home » Thus, the number of distinct ways is \(\boxed31\). - 500apps

Thus, the number of distinct ways is \(\boxed31\). - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Therefore, there is **no two-digit** such number.

📌 But perhaps the question meant **three less than a multiple of 7, or 8, or 9**, but that would be too weak.

📌 Alternatively, maybe it meant a number such that $ x + 3 $ is divisible by **each** of $ 7, 8, 9 $ individually, but not necessarily simultaneously. But that’s redundant — divisibility by each implies divisibility by their LCM.

📌 Thus, no solution exists in two digits.

📌 But for olympiad style, perhaps the intended setup was different. Let’s reframe: suppose the number is **three less than a multiple of 7 and 8**, but not necessarily 9? But question says of 7,8,9.

📌 Alternatively, maybe the number is three less than a multiple of **the lcm**, but we already saw $ x = 501 $ is minimal.

📌 But since the problem asks for a **two-digit** integer, and none exists, perhaps the intended answer is that **no such number exists**, but that’s not typical for olympiads.

📌 Wait — perhaps we made a directional error. Let's suppose the number is **three less than a multiple of each**, but again, same.

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