Project Euler #113: Non-bouncy numbers

  • + 1 comment

    I arrived at the formula (k+9)C9+(k+10)C10 - 10*k - 2 non bouncy numbers less than 10^k using pen and paper. (combinatorics)

    Also number of increasing and decreasing non bouncy numbers won't be the same, some people might make that mistake.

    • + 0 comments

      Indeed, it may help to understand Rota's famous 12-fold way of counting functions N⟶X.

      For the second sentence, I agree and my further hint is to count a space " " as a digit higher than 9 when counting the decreasing sequences recursively. For example, "10" is a decreasing 2-digit number but padding a leading zero "010" switches it to bouncy, whereas padding it with a high-valued leading space makes it " 10", thus retaining it as decreasing.