We must admit that we're not all that fond of crowds (leaving aside baseball games, of course), preferring the tranquil solitude of the prairie, the desert, or the open sea. But at times, it's just impossible to avoid jostling with massed humanity as we go about our business in one urban environment or another.

Today's problem presents us with a crowd scene of a different sort, as we view a checkerboard situation where the White forces are a full three men up on the Black side, yet a win seems elusive. This unexpected turn of events is due to some severe single-corner crowding, where a lone Black king is holding three White pieces completely at bay.

Here's the position:

BLACK

WHITE
White to Play and Win

W:WK4,8,K12,13,22:BK3,K14.

White doesn't seem to have a single decent move, yet the game can still be won, though it's every bit as difficult as making your way along Kalakaua Avenue on a Saturday evening.

Try to solve the problem, but if your thoughts become overcrowded, relieve the congestion by clicking on Read More to see the solution.

This time of year it is our wont to observe that in the Northern Hemisphere the days are long and hot, and folks are out enjoying summer. So our August speed problems this time are most definitely on the easy side, and solving them won't cut into your pool or picnic time.

In fact, just to be sure that you have plenty of time for the summer pursuits of your choice, we're setting the time limit for these problems to a mere ten seconds. Don't blink twice, you may be too late! Click on the links below to show the problems and start the clock on your ten second solving time.

August Speed Problem One (very easy)

August Speed Problem Two (very easy)

Check your solutions by clicking on Read More, and then go back to your enjoyment of a fine summer day.

Editor's Note: To our friends in the Southern Hemisphere, who are mired in the depths of winter, we can only point out that in less than six months the tables will be turned.

Joshua Sturges was one of the early great teachers in the world of draughts; he published his "Guide to the Game of Draughts" in London, in 1800, and for nearly half a century it was the draughts primer. Even to this day, online bookseller Amazon lists the title in their catalog as Joshua Sturges's guide to the game of draughts: In which the theory and practice of that scientific recreation are clearly illustrated including one hundred and seventy-two critical positions. They list the date as 1881, for some reason (there were apparently numerous later editions and reprints), and note that the title is not currently available, and is not expected back in stock!

Information on Mr. Sturges isn't all that easy to come by, but we did find this historical record of a London jury that convened in July, 1801.

In the listing of jury members, a Joshua Sturges is shown as a member of the "Second Middlesex Jury." We don't know if this is the same Mr. Sturges of draughts fame, but given the date and location, it is certainly quite possible.

But today, in our continuing Checker School series, we're asking you to be both judge and jury of the following Sturges "situation."

J. Sturges
BLACK

WHITE
White to Play and Win

W:WK19,K22,30:B12,21,K27.

Certainly, White is better off here, but demonstrating the win makes all the difference, and it will certainly require care and attention.

Weigh the evidence and come up with the verdict: can you prove that White wins or will there be a hung jury? After you've given it your best effort, click on Read More to see the solution, notes, and several example games, as provided by Ben Boland.

Continuing with our ongoing series taken from Willie Ryan's Tricks Traps & Shots of the Checkerboard, this month we present a complex problem that Willie himself admired greatly, as he clearly states below.

"No compendium of classical coups would be complete without including the historical Horsefall Stroke, which I consider one of the great masterpieces of scientific play. Here's the run-up:

WHITE

BLACK
Black to Play and Draw

A---Weak, but drawable. The following makes an easier draw: 3-8, 19-15, 2-7, 22-17, 7-10, 17-13, 10-19, 26-22, 19-26, 30-23, 14-17, 21-14, 11-15, 18-4, 9-18, 23-14, 6-9, etc.

B---Strongest, forming position illustrated. If instead of 8-11, white moves 25-22, the only moves to draw are: 7-11*, 8-6, 2-9, 22-18, 9-13*, 18-14, 13-17, 14-10 (23-18, 21-25, 30-21, 19-24 results in a draw), 5-9, 23-18, 9-13, 18-15, 17-22."

We're well beyond the introductory material in Mr. Ryan's classic book, so you can't expect an easy ride. Don't horse around; try to rein in the problem, and then click on Read More to gallop directly to the Willie's solution.

Checkers has been solved. This headline has appeared in many news articles in the past few days, as Dr. Johnathan Schaeffer announced on July 19, 2007, that his team at University of Alberta has completed their quest to develop a rigid proof that checkers is, with perfect play on both sides, a drawn game.

This proof is a monumental achievement in computer science and took years of work to develop. The proof is non-trivial, both in complexity and quality; Dr. Schaeffer's team not only proved that checkers is a draw, they've shown how to do it. Given that you have a very powerful computer, an enormous database, and some sophisticated computer code, you can draw all your games from now on.

What's our reaction to this? As computer literates ourselves, we're most impressed with Dr. Schaeffer's work. As checker players and fans, we can only say, "Let's play checkers." In fact, this week your editor himself was quoted in Nature Magazine, when asked about the impact of this new proof on the checker playing public, as saying, "People will keep right on playing checkers."

And, of course, they will.

We note that, while checkers is now known definitively to be a draw, this coming week's U.S. National Tournament hasn't been canceled, and we in fact predict with great confidence that the tournament will produce some really fine games of checkers. Too, we have no plans to discontinue publishing The Checker Maven as we still think there are plenty of checker topics worthy of column space.

While the computer has had a profound influence on our game, mostly (but not entirely) for the good, checkers is in the end a game for people. Real, live people from all walks of life play checkers, and they won't stop now. From country picnic tables all the way to Las Vegas tournament halls, checkers will go on.

A draw? Yes, in theory, the game is a proven draw. In practice, it's still a great deal of fun and a tremendous intellectual challenge, and that's not going to change.

Editor's note: The photo at the top of this article is a file photo and is not of Dr. Schaeffer and his laboratory.

The publication date of today's article is July 14, which is the French national holiday, most popularly known here in the US as Bastille Day. The French certainly know how to throw a party, and music, dancing, liberally quaffed libations, parades, and much more take place throughout the country starting the evening of July 13 and continuing all through the next day. Capping it all off, of course, are spectacular displays of feu d'artifice--- fireworks.

We wanted to publish a French problem to celebrate the occasion, but high-level checkers as played in France is almost exclusively the international game, played on a 10x10 board with rules that differ in substantial ways from the Anglo-American game about which we write here. So instead, we're offering our own feu d'artifice display, featuring spectacular fireworks on the checker board. Here's the position, as composed by problemist T. Duncan.

BLACK

WHITE
White to Play and Win

W:W8,K11,K15,18,22:B4,9,13,25,K29.

With a setup such as this, you just know something extraordinary is about to happen. Can you work it out?

There's no need to explode, of course; clicking on Read More will rocket you to the crowd-pleasing solution.

Albuquerque, New Mexico, is perhaps an hour's drive south on Interstate 25 from our Santa Fe offices. We go there frequently, and with our eye for the unusual, we've spotted some rather unique combinations during our visits.

Where else will you find a Mexican-Greek restaurant?

Or a muffler repair shop that also houses a Vietnamese lunch counter?

It's not possible to top either of these eclectic melanges, but our checker problem today is a combination of a different sort.

For the sake of variety, on the first Saturday of each month we've alternated between speed problems and stroke problems. This time, we present a single problem that has aspects of both: you'll need to find the winning stroke in a rather short amount of time. The problem is fairly easy, and we think fifteen seconds should leave you with time to spare.

Of course, we're as infamous for our diabolical notion of "easy" as our Javascript clock is infamous for its unforgiving nature. But in any case, combine speed, clear thinking, and accurate play to solve this month's speed/stroke problem.

July Speed Problem

When you've worked it all out, click on Read More for the very pleasing solution paired with the actual game from which the position arose. Though we can't offer you tacos, gyros, a new muffler, or Vietnamese noodle soup, we do think you'll enjoy today's problem.

Hawaiian Konane Board Carved in Rock

Ed Gilbert generously sent along a copy of his 10-piece KingsRow endgame database (see previous story) for the use of The Checker Maven, and we've been having a few pleasant adventures getting it all set up and ready to use. We in turn send our thanks to Ed for supporting our ongoing work of bringing checkers to the public each and every week.

Our general policy is not to solicit donations and not to accept them if offered, as we believe that The Checker Maven should be free for everyone, and we don't want to have class distinctions between donors and non-donors. But Ed's offer was very special and very much appreciated. (We did also once accept a generous donation from Brian Hinkle, which is subsidizing a future electronic republication of a classic checker book.)

To install Ed's database, we really needed a faster and larger computer system, so, at Ed's advice, we built one from an assemblage of parts ordered from the component vendor Newegg. It took a little time and effort but our new system is running fine. We've called it Konane Kane which in Hawaiian roughly means Checker Dude. (The game Konane is sometimes called "Hawaiian Checkers.")

Here's a picture of the new system in the basement laboratory of our Santa Fe offices.

"Konane Kane" in our Santa Fe Computer Laboratory

Sometime later next year, Konane Kane will likely travel to "Hawai`i nei" and become the main computer at our Honolulu offices. In the meanwhile, we'll be using it and Ed's phenomenal database to bring you exciting new features and articles. It's a big win all around. Mahalo nui loa!

Who among us has not read The Autobiography of Benjamin Franklin, and derived untold benefit from the eminently practical wisdom and philosophy of its author? And who would be surprised to learn that Ben Franklin was himself a checker player, who praised the merits of the game as training for life?

Today's Checker School problem, though, was composed by a different Benjamin: E. A. Benjamin, to be precise, but we think it's as practical and useful, at least in checker terms, as Ben Franklin's advice for living a successful life. The problem situation is shown below.

E. A. BENJAMIN
White

Black
Black to Play and Win

B:W28,K9,K4:BK20,19,3.

Taking a closer look, we see that White has a material advantage, having two kings to Black's one, but Black's mobility is clearly superior. Is it enough to turn the situation into a Black win? Try it out, and then click on Read More for the solution, notes, a sample game, and some words of wisdom from the better-known Benjamin.

It was our pleasure quite recently to receive in the mail a copy of a wonderful new checker book, John Cardie's How to Beat Granddad at Checkers, and we simply can't say enough good things about it.

Mr. Cardie's book is based partly on the premise that grandparents have a lot to offer to grandchildren, and that many important lessons can be imparted over the checkerboard. So, to a large extent, the book is about much more than checkers: it's about life, and wisdom, and family, and learning, and teaching. It's about precious hours that grandparents and grandchildren can spend together and about the wonderful and irreplaceable memories that these moments create. Mr. Cardie's book speaks to the heart as much as to the mind.

Of course, there's checker content galore, and grandparents will likely learn a great deal themselves. After an introduction which convincingly explains why checkers is a good thing for both grownups and youngsters, Mr. Cardie teaches about the numbered board and checker notation, and then jumps right into basic checker tactics. (Presumably, grandparents can teach the rules and other basics on their own, although there is a later chapter in the book with the official rules of checkers.) Mr. Cardie has invented some very clever new names for old tactics, such as "the sandwich move" for what is traditionally known as "breeches." Some of the names are really catchy, such as "Twins in the Closet" for a particular three king vs. two king endgame. The book as well is liberally sprinkled with pages of general instruction, such as lessons on sportsmanship, and interestingly titled items like "Earnings and Yearnings" and many more, which use checkerboard situations as analogues for life. There are a number of checker puzzles of appropriate difficulty; and a listing of checker websites and resources rounds out the volume.

Some time back, we reviewed Galina Golant's excellent book, Play Checkers With Me. Ms. Golant's book was at the small child, introductory level. Mr. Cardie's book is the next step up, and is suitable for use with children who are a few years older, perhaps from the age of six or seven onwards. But there is no question that adults too will enjoy the book and benefit from it.

We hear that Mr. Cardie may be able to land a national distribution contract for the book through a prominent chain. We're sworn to secrecy about the details, but we certainly hope that comes to pass.

Author John Cardie

Obtaining this book is easy and inexpensive, and something that we recommend you do without delay. Just go to Mr. Cardie's website at www.checkerscreateskings.com for full details on ordering options. It's a book that is not to be missed.