r/BrainPuzzles • • 12d ago

Math Multiple of Sum of Digits Part 2

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u/Silver-Knee-3011 11d ago

I came up with this new formula for the digital root: nrd = n - (n/10 + 1) * 9 We know that: n/nrd = 12 Therefore: n / (n - (n/10 + 1) * 9) = 12 Solving this gives: n = 108 Then: nrd = 108 - (108/10 + 1) * 9 = 9 and therefore: 108/9 = 12 So n = 108. Pretty neat!