Check out Alice Chess, our featured variant for June, 2024.

Enter Your Reply

The Comment You're Replying To
Sam Trenholme wrote on Sat, Jul 14, 2007 07:28 AM UTC:
Looks like you're right. I will draw it out:

  • First, we place the bishops. There are 2025 ways of arranging the bishops.
  • Next, we place the knights. For each arrangement of bishops, there are 1820 ways to put the knights on the board.
  • Next, we place the rooks. For each arrangement of bishops and knights, there are 495 ways to place the rooks.
  • Next, we place the Archbishops. For each arrangement of the minor pieces, there are 28 arrangements for the archbishops.
  • Next, we place the Marshalls. For each arrangements of all of the above pieces, there are 15 Marshall setups.
  • Next, we place the Queens. For all of the above setups, there are 6 ways to have the queens on the board.
  • Next we place the king. There are two places he can go. However, this is balanced by the fact we remove all mirror images.
2025 * 1820 * 495 * 28 * 15 * 6 = 4,597,292,700,000

Sorry it took so long to verify your number. This is the first time I have had a computer with an arbitrary precision calculator and net access at the same time in a while (Let's hear it for Ubuntu live CDs).

Edit: Yes, 64-bit computer owners, the above number can easily be calculated using 64-bit integers. I'm still in the 32-bit stone age. Do they even make 64-bit laptops that weigh less than 6 pounds?

Edit Form

Comment on the page Complexity of Large Variants

Conduct Guidelines
This is a Chess variants website, not a general forum.
Please limit your comments to Chess variants or the operation of this site.
Keep this website a safe space for Chess variant hobbyists of all stripes.
Because we want people to feel comfortable here no matter what their political or religious beliefs might be, we ask you to avoid discussing politics, religion, or other controversial subjects here. No matter how passionately you feel about any of these subjects, just take it someplace else.
Avoid Inflammatory Comments
If you are feeling anger, keep it to yourself until you calm down. Avoid insulting, blaming, or attacking someone you are angry with. Focus criticisms on ideas rather than people, and understand that criticisms of your ideas are not personal attacks and do not justify an inflammatory response.
Quick Markdown Guide

By default, new comments may be entered as Markdown, simple markup syntax designed to be readable and not look like markup. Comments stored as Markdown will be converted to HTML by Parsedown before displaying them. This follows the Github Flavored Markdown Spec with support for Markdown Extra. For a good overview of Markdown in general, check out the Markdown Guide. Here is a quick comparison of some commonly used Markdown with the rendered result:

Top level header: <H1>

Block quote

Second paragraph in block quote

First Paragraph of response. Italics, bold, and bold italics.

Second Paragraph after blank line. Here is some HTML code mixed in with the Markdown, and here is the same <U>HTML code</U> enclosed by backticks.

Secondary Header: <H2>

  • Unordered list item
  • Second unordered list item
  • New unordered list
    • Nested list item

Third Level header <H3>

  1. An ordered list item.
  2. A second ordered list item with the same number.
  3. A third ordered list item.
Here is some preformatted text.
  This line begins with some indentation.
    This begins with even more indentation.
And this line has no indentation.

Alt text for a graphic image

A definition list
A list of terms, each with one or more definitions following it.
An HTML construct using the tags <DL>, <DT> and <DD>.
A term
Its definition after a colon.
A second definition.
A third definition.
Another term following a blank line
The definition of that term.