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Which four-digit number is three times the sum of all two-digit combinations that can be made of its digits?
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Just thinking out loud to myself here.\[a,b,c,d\in\mathbb Z\\1000a+100b+10c+d=3\left(a^2+ab+ac+ad+b^2+bc+bd+c^2+cd+d^2\right)\]Mmm...
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