# Only 1 and 2

Number Theory Level pending

A positive integer with $$20$$ digits is a interesting number if it only has the digits $$1$$ and $$2$$. (For example, the $$1222212212112121112$$ is an interesting number.

Find the maximum value of $$k$$, such that there exist $$k$$ interesting numbers where every pair of them differ in at least 3 places.

For example we cannot write both $$111\dots1112$$ and $$1111\dots1222$$, but we can write down $$121212\dots121212$$ and $$212121\dots212121$$.

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