【整数問題】文字を数字に変える【N進法】

#NumberSystem #IntegerProblems #JuniorHighSchoolEntranceExam #Arithmetic #CriticalThinking ■ Problem abc(5) = cba(7) Express the numbers that satisfy the above equation in base 10. ■ Approach Convert each number to base 10. ■ Expansion abc(5) = 25a + 5b + c ■ Next cba(7) = 49c + 7b + a ■ Equation 25a + 5b + c = 49c + 7b + a ■ Rearrangement 24a − 2b − 48c = 0 ■ Divide by 2 12a − b − 24c = 0 ■ About b b = 12a − 24c ■ Numerical Conditions Since it's base 5 a, b, c are between 0 and 4 However, a ≠ 0 ■ Range of b 0 ≤ b ≤ 4 Therefore 0 ≤ 12a − 24c ≤ 4 ■ Rearrangement 12(a − 2c) must fall within the range of 0 to 4. The only multiple of 12 that falls within this range is 0. ■ Therefore a − 2c = 0 → a = 2c ■ Candidates c=1 → a=2 c=2 → a=4 c=3 → a=6 (Not possible) ■ When c=1 a=2 b=0 ■ Verification 201(5) = 2×25 + 1 = 51 102(7) = 49 + 2 = 51 OK ■ When c=2 a=4 b=0 ■ Verification 402(5) = 4×25 + 2 = 102 204(7) = 2×49 + 4 = 102 OK ■ Conclusion 51 and 102 ■ Key Points Convert the number base to decimal. Don't forget the digit limit. Narrowing down the range is key. This is a very beautiful and well-designed problem that combines number bases and integer manipulation. 🔗 Related Videos & Recommended Links [Junior High School Entrance Exam: Math Calculation Problem Explanation Series] ▶    • 灘中入試問題 2005年度1日目｜素因数分解で分数の計算問題   [Junior High School Entrance Exam: Practice Problems on the Properties of Integers] ▶    • 【魔方陣の攻略法】真ん中の数の見つけ方！公務員試験＆中学受験の数的処理対策｜算数過去...   [Kaisei Junior High School Entrance Exam Problems & Past Paper Explanation Series] ▶    • 【開成中学の算数】単位分数の和と整数問題を徹底解説！2010年度過去問に挑戦｜中学受験算数   [Nada Junior High School Entrance Exam Problems & Past Paper Explanation Series] ▶    • 灘中入試問題 2005年度1日目｜素因数分解で分数の計算問題   📢 A Request to Viewers If you found this video helpful, please let us know by liking or commenting! We also welcome requests for explanations of other problems! 📌 About This Channel This channel provides methods for steadily improving the skills necessary for entrance exams while learning arithmetic and mathematics in a fun way. We fully support everyone who wants to "train their thinking skills" and "overcome their weaknesses"! 📩 Business Inquiries/Contact For interview and business inquiries, please contact us here: 📧 [email protected] #JuniorHighSchoolEntranceExam #EntranceExamArithmetic #Mathematics