We have $10^K$ road signs (numbered 0 through $10^K−1$).
For each valid $i$, the sign with number $i$ has the integer $i$ written on one side and $10^K−i−1$ written on the other side.
We need to find how many road signs have exactly two distinct decimal digits written on them (on both sides in total)?
For example, if $K=3$, the two integers written on the road sign $363$ are $363$ and $636$, and they contain two distinct digits 3 and 6, but on the road sign $362$, there are integers $362$ and $637$, which contain four distinct digits — $2, 3, 6, 7$. On the road sign $11$, there are integers $11$ and $988$, which contain three distinct digits — $1, 9, 8$.
Devise a procedure to find the number of road signs for any given value of $K$.