# String Of Digits

Let $$S = \langle s_1, s_2, s_3, \dots \rangle$$ be a string of $$N$$ digits (0 through 9) with the following property:

For any three distinct digits $$a, b, c$$, there is an index $$1 \leq n \leq N-2$$ such that $$\{s_n, s_{n+1}, s_{n+2}\} = \{a, b, c\}$$. In other words, every set of three distinct digits occurs as a substring in $$S$$ but not necessarily in that order.

What is the length $$N$$ of the shortest string $$S$$ with this property?

Note: It is not difficult to estimate a lower bound for $$N$$; but there is no guarantee that a string of that length actually exists...

Examples and Assumptions

A set of three digits may occur as a substring of $$S$$ more than once.

In the string abceabdeacdebcd each subset of the three letters $$\{a\dots e\}$$ occurs at least once. The subset $$\{b, c, e\}$$ occurs twice, once as bce near the beginning and once as ebc near the end.

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