# Base of number base

Number Theory Level 2

There is a number $$a$$, which can be written as $$\overline{xyz}$$ in base 9 and $$\overline{zyx}$$ in base 6, for some positive integer $$x,y,z$$. Find $$x+y+z$$.

Details and Assumption

$$\overline{xyz}$$ represents a 3-digit integer such that it is equal to $$100x+10y+z$$ for $$x,y,z$$ are non-negative integers and $$0 \le x,y,z \le 9$$.

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