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



Solution


13. ... 24-20
14. 8-12

7-11 looks like a possible defense but it doesn't work: 7-11 14-10 2-7 10-6 9-13 25-22 18x25 30x21 11x18 20x2 White Wins.


14. ... 20x11
15. 7x16 15-10
16. 3-8 10-6
17. 9-13 6-1
18. 16-19 14-10

White wins. There is no way to stop White from winning a man.

09/24/16 - Category: Books - Printer friendly version
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