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2025 AMC 10BProblem 4P1-10~2 minPrint
Bases & DigitsDiophantine EquationsSplit into exhaustive cases and handle eachSet up the equation/formula and compute; no special trick needed

The value of the two-digit number a‾ b‾\underline{a}~\underline{b} in base seven equals the value of the two-digit number b‾ a‾\underline{b}~\underline{a} in base nine. What is a+b?a+b?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.