A number theory problem by Amenreet Singh Sodhi

Let a b c d e f \overline{abcdef} be a six digit integer such that that the other six digit integer, d e f a b c \overline{defabc} is 6 times the value of a b c d e f \overline{abcdef} . Find the value of a + b + c + d + e + f a+b+c+d+e+f .


The answer is 27.

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