# A Unique 10-digit Number

There exists a unique 10-digit number $$\overline{abcdefghij}$$ which contains each of the digits 0, 1, 2, $$\dots$$, 9 exactly once, such that for each $$k$$, $$1 \le k \le 10$$, the number formed by the first $$k$$ digits of $$\overline{abcdefghij}$$ is divisible by $$k$$. For example, for $$k = 4$$, the number $$\overline{abcd}$$ is divisible by 4.

Find the three-digit number $$\overline{abc}$$.

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