The Checker Maven

The 4th Catalan Number

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As we continue to explore the Kelso opening with Willie Ryan and his classic book Tricks Traps & Shots of the Checkerboard, we reach our 14th installment on this fascinating opening.

There's almost nothing special about the number 14, except perhaps that it's what's known as a Catalan number, the 4th Catalan number, to be precise. Catalan numbers are named for Belgian mathematician Eugène Charles Catalan, and appear in various applications in the branch of mathematics known as combinatorics. The simple(!) formula for Catalan numbers is given above. Catalan numbers also appear in graph theory; in particular, Cn is the number of non-isomorphic ordered trees with n vertices, as also shown above. (If you don't quite follow that, watch the movie Good Will Hunting.)

But enough math! By now you're surely ready for some checkers. Here's the run-up to today's position.


1. 10-15 22-18
2. 15x22 25x18
3. 6-10 18-14
4. 10x17 21x14
5. 9x18 23x14
6. 1-6 29-25
7. 12-16 26-23
8. 16-19 24x15
9. 11x18 28-24
10. 8-11 31-26

Willie offers 31-26 as an alternative to 24-19, the latter of which he calls "A natural though timid move."


11. 4-8 23-19
12. 6-919-15
13. 11-16

Willie correctly says that 9-13 should have been played here and that now "Black will have to do more than whistle to get past the graveyard."

BLACK
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WHITE
White to Play and Win

W:W32,30,27,26,25,24,15,14:B18,16,9,8,7,5,3,2.

Higher math skills are not required here, just rather high over the board checker skills. This is not an easy problem, but there is still no need to apply combinatorics or graph theory (unless you really want to), as you can always check your solution by simply clicking your mouse on Read More.20050904-symbol.gif

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09/24/16 - Printer friendly version
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More Than One Way To Do It

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"There's more than one way to do it" is a common enough phrase, and it seems to have gotten attached to the scripting language Perl, due to Perl's extreme (some say excessive) flexibility. At The Checker Maven Perl scripts figure prominently in our computer work, and, even though the modern trend is more towards the Python language, we persist. But that discussion is even further off-topic.

Today's problem, submitted by regular contributors Lloyd and Josh Gordon of Toronto has two main solutions, hence "more than one way to do it." One of the solutions occurred in over the board play, while the other, which is quite different, is due to KingsRow computer analysis.

BLACK
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WHITE
White to Play and Win

W:W30,23,22,19,16:B14,12,10,7,6.

Which solution will you find? Can you see them both? To find out, there's only one way to do it: click on Read More.20050904-symbol.gif

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09/17/16 - Printer friendly version
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Cowan's Coup Revisited

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Artwork courtesy La Mame Games

Just over five years ago, we published a column on Cowan's Coup based on analysis by Willie Ryan. This week in our Checker School entry, we'll revisit the position and gain the benefit of Ben Boland's viewpoint, as expressed in his classic Famous Positions in the Game of Checkers.

WHITE
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BLACK
White to Play and Draw

W:W24,23,21,20,19,18:B17,14,12,11,10,9.

No matter what move White makes, he's going to lose two men at once. Yet we're asked to find a move that draws.

Is this a coup that you can pull off? Please do try; after all, this is a non-violent coup. But if the solution eludes you, or you'd just like more insight, you can click on Read More to see one way to do it along with numerous sample games and an explanatory note or two.20050904-symbol.gif

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09/10/16 - Printer friendly version
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Labor Day Salute

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Labor Day; it's a welcome day off work, a last hurrah for summer in North America, a time to see a parade, or squeeze in one more barbecue or picnic or camping trip before the leaves fall and the nights become chill.

And, as we point out each year, it's a time to show our respect for the average Jane and Joe that make up America's workforce, those honest, decent, hard-working people who show up every day, do their jobs, and help make America what it is. There was a time when checkers was their game, and although that's less of a truism today, checkers remains democratic, accessible, and suitable for everyone.

On holidays like these, we like to feature great American players and problemists. Today we have one of the few problems authored by one of the greatest American checkerists of all time, Samuel Gonotsky. It is based on actual over the board play.

BLACK
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WHITE
White to Play and Draw

W:W32,31,26,23,K14,13:BK30,28,24,20,19,16,15.

White is a man down but has mobility advantages. Can the situation be turned into a draw? Labor away at this one; but seeing the solution is hardly laborious and requires only a mouse click on Read More.20050904-symbol.gif

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09/03/16 - Printer friendly version
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