Neat. Let’s see 
some solutions. 🤗 it’s a cool problem I have to admit lololol
+26379 solutions
There are 21 possible sequences of steps that take the counter form square 1 to square 10.
\(\begin{array}{|r|l|} \hline 1.& (1\ 2\ 4\ 5\ 7\ 8\ 10) \\ 2.& (1\ 2\ 4\ 5\ 7\ 10) \\ 3.& (1\ 2\ 4\ 5\ 8\ 10) \\ 4.& (1\ 2\ 4\ 7\ 8\ 10) \\ 5.& (1\ 2\ 4\ 7\ 9\ 10) \\ 6.& (1\ 2\ 5\ 6\ 9\ 10) \\ 7.& (1\ 2\ 5\ 7\ 8\ 10) \\ 8.& (1\ 2\ 5\ 7\ 10) \\ 9.& (1\ 3\ 4\ 6\ 7\ 9\ 10) \\ 10.& (1\ 3\ 4\ 6\ 7\ 10) \\ 11.& (1\ 3\ 4\ 6\ 9\ 10) \\ 12.& (1\ 3\ 4\ 7\ 8\ 10) \\ 13.& (1\ 3\ 4\ 7\ 9\ 10) \\ 14.& (1\ 3\ 6\ 7\ 9\ 10) \\ 15.& (1\ 3\ 6\ 7\ 10) \\ 16.& (1\ 4\ 5\ 7\ 8\ 10) \\ 17.& (1\ 4\ 5\ 7\ 10) \\ 18.& (1\ 4\ 5\ 8\ 10) \\ 19.& (1\ 4\ 6\ 7\ 9\ 10) \\ 20.& (1\ 4\ 6\ 7\ 10) \\ 21.& (1\ 4\ 6\ 9\ 10) \\ \hline \end{array}\)
