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Adding bases

Let \(a_b\) denote \(a\) in base \(b\).
Find bases \(A\), \(B\) and \(C\) less than 10 such that \(12_A+34_B=56_C\).

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Tags: numbers, bases
If you enjoyed this puzzle, check out Sunday Afternoon Maths VIII,
puzzles about bases, or a random puzzle.

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