Sorry, but your calculation is significantly too simple. An illegal board can fail more than just one constraint. Your 2*48*6*6**61 enumerates the possible paths for a simple algorithm that is guaranteed to produce an illegal board. But a huge number of those paths are just different ways of generating the same board (if a board violates 6 different constraints, then your equation will count that board 6 different times).

So you have over estimated the number of illegal boards rather significantly. This is rather easy to see by noting that your estimated number of legal boards comes out to -360*6**61. A negative number of possibilities is clearly the wrong answer.

I've computed counts for similar sets in the past. It gets very complicated very quickly. I'll try to write up at least the first part of such a calculation but I doubt I'll be posting that very soon. :)

You could get an approximate answer by generating a large number of boards at random and calculating the average number of constraints violated by a random illegal board and then using that number to divide the number you originally calculated.

- tye        

In reply to Re^2: Pattern enumeration. (KISS) by tye
in thread Pattern enumeration. by BrowserUk

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.