The Lumber Room

"Consign them to dust and damp by way of preserving them"

Serieshelpmate in 19

with 2 comments

Here’s a brilliant problem.

Consider the following chess position.

Black is to make 19 consecutive moves, after which White checkmates Black in one move. Black may not move into check, and may not check White (except possibly on his last move). Black and White are cooperating to achieve the aim of checkmate. (In chess problem parlance, this problem is called a serieshelpmate in 19.) How many different solutions are there?

This problem is due to Kauko Väisänen, and appears in A. Puusa, Queue Problems, Finnish Chess Problem Society, Helsinki, 1992 (Problem 2).

Hint: the above is quoted from Richard Stanley’s Enumerative Combinatorics.

About these ads

Written by S

Sun, 2011-05-29 at 15:30:25 +05:30

Posted in mathematics

2 Responses

Subscribe to comments with RSS.

  1. Nice one Shreevatsa!! I found one solution inside of a minute, and am too lazy to think of others. How many are there? :)

    S P Suresh

    Thu, 2011-06-09 at 21:10:04 +05:30

    • Thousands! :-)
      [In some sense the solution you found is unique "up to" something, but the actual number is in the thousands. And there's a nice way of counting them...]

      S

      Fri, 2011-06-10 at 00:28:30 +05:30


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

Join 67 other followers