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@selina
Good instinct to start with smaller variants of the problem and working your way up.

You've chosen a perhaps confusing way of directly tackling the big length=14 problem, by partitioning it as "how big is the set of 14-digit numbers with exactly that many 2s".

Note that you can start smaller and simpler, by just considering shorter-length numbers first.

As you work the shorter examples, you may see a pattern in construction, or a pattern in the numbers. Either intuition will help you.
Dr Matrix
on /blog/97
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