# Parlour Magician

﻿In a parlour game, the “magician” asks one of the participants to
think of a three-digit number $${ abc }_{ 10 }$$. Then the magician asks the participant to add the five numbers $${ acb }_{ 10 }$$, $${ bca }_{ 10 }$$, $${ bac }_{ 10 }$$, $${ cab }_{ 10 }$$ and $${ cba }_{ 10 }$$, and reveal their sum. Suppose the sum was $$3194$$. What was $${ abc }_{ 10 }$$ originally?

Details and Assumptions

$${ abc }_{ 10 }$$ means a 3-digit number with $$a,b,c$$ as it's digits and not $$a\times b\times c$$.

This problem is not original.

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