Sal Westerman, of Bismarck, North Dakota, was doing what he did every summer.

It was July of 1955 and Sal and his wife, Sylvia, were spending a couple of weeks at a lakeside cabin near Lake Sakakawea. For years they had rented the same cabin for the same two weeks.

Sal of course missed his Saturday afternoon visits to the Beacon Cafe in Bismarck, where his Coffee and Cake Checker Club met weekly during fall, winter, and spring. But like most such things in North Dakota, there was a pause to enjoy the all-too brief summer season, and the club wouldn't meet again until the Saturday after Labor Day.

At the lake, Sal and Sylvia didn't follow any particular schedule. They went to bed when they were tired, got up when they were ready, went on walks, relaxed on the porch, and just took it easy. Sal, of course, brought along some checker magazines.

This morning, however, Sal decided to take a rowboat out on the lake and try some fishing. At least, that's what he called it. What he actually did was row the boat out a ways, drop a line in the water, and then get out a checker magazine. If a fish bit that was fine but he really didn't care. Sylvia, of course, always hoped he'd catch something to cook for dinner, but she knew Sal's habits and tricks and didn't count on anything.

It was a clear and sunny morning, and it was going to be hot, so Sal knew he should go out early. The fish wouldn't really be biting once the temperature rose, but worst of all was that it would be just too warm out in the sun to focus on his magazine. So Sal rowed out at 7 AM right after an early breakfast.

"Good luck, dear," Sylvia had said, not failing to notice the copy of All Checkers Digest in Sal's tackle box.

It was still nice and cool when Sal put a lure on his hook and cast out his line. Then with a smile of anticipation, he opened up his magazine. Sal loved all the news, features, and analyzed games from professional play, but he especially enjoyed the checker problems, and this issue featured one by his friend Ed from Pennsylvania. Opening up the magazine, he quickly found the problem and was soon absorbed in trying to work out the solution.

He was deep in thought when he heard the line on his fishing reel start to run out at a rapid pace. There was a fish on his hook and it must have been a big one!

He set his magazine down on the seat beside him and took his pole from its holder. The fish was still running out as his started to crank on his reel, trying to pull it back in. It was a back and forth tussle and after about five minutes both the fish and Sal were starting to tire. Slowly but surely, Sal was making headway, pulling the fish closer and closer. Soon he could see the fish almost next to the boat, near the surface of the water. Now, where was that fish net ...

While still holding his pole with one hand, Sal reached down and grabbed the handle of his net. He pulled it up ... and wouldn't you know it but the end of the net hit his checker magazine and knocked it into the water!

Sal dropped his pole into the boat and reached out with his net to try to catch his magazine, which was slowly starting to sink. Completely forgetting about the fish, he went desperately for the magazine, but it was too late. The magazine had sunk out of reach. For a moment Sal thought about diving into the water after it, but at 73 years old diving into cold lake water wouldn't have been a good idea, and if he caught a cold from it he'd get the dickens from Sylvia.

Finally remembering the fish, he turned to the other side of the boat. But by this time, it seemed, the fish had somehow wriggled off the hook and was gone.

Despondent, Sal rowed back to shore, moored the boat, and went back into the cabin.

Sylvia was at the kitchen table doing a crossword puzzle. "Back so soon, dear? Any luck?"

Sal slowly recounted the story of the big one that got away, and the lost copy of All Checkers Digest.

"Oh, Sal, I'm so sorry you lost the fish. It would have made such a nice dinner. And the magazine, too, although I know you brought along several others."

"Yes, I did," Sal replied, "but this was the latest issue, and I was just starting to make progress on this problem by Ed ... "

"It's a shame, dear, but I'll make you a nice dinner tonight and you'll feel better about everything, I'm sure. How about a macaroni and hamburger hot dish?" Sylvia knew that was one of Sal's favorites, and she spiced it up with some tangy cheese.

"Oh, yes, dear, thank you, that would be wonderful." But Sal still looked despondent.

It was about time for lunch and they had a ham sandwich with some canned tomato soup. Sal then announced he would take a short rest and Sylvia said she would need to drive into town to pick up some ground beef and a package of macaroni for tonight's dinner.

After washing dishes, Sal lay down while Sylvia headed off for town. Sal awoke an hour or so later and Sylvia was just coming back into the cabin with a bag of groceries.

"Unpack for me, will you Sal, while I freshen up a little. It's so hot out now!" Sylvia said, placing the bag on the kitchen table.

"Sure," Sal said.

Macaroni went into the cupboards, ground beef into the refrigerator, and so on. "Quite a lot of groceries," Sal remarked, but got no reply.

Wait ... what was that in the bottom of the brown paper shopping bag?

No, it couldn't be. Sal had to look twice, then a third time. Slowly, he took the item out, looking at it in wonder.

"Surprised, dear?" Sylvia asked, now standing at the dining table.

"My goodness," Sal said, "how did you do it?"

"Oh, it wasn't hard. It's a pretty popular item, after all. Just about everyone carries it."

Sal smiled as he looked lovingly first at his wife, and then at the copy of the latest issue of All Checkers Digest that he held in his hands.

---

It looks as though Sal is going to get to try to solve that special problem after all, and of course you can, too. After you've tried it, though, there's no need to go fishing for the solution; just cast your mouse on Read More to see how it's done.

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In today's Checker School column, we're going full-bore academic. Here's the abstract from a recent paper entitled When Problem Solving Followed by Instruction Works: Evidence for Productive Failure by Tanmay Sinha and Manu Kapur.

"When learning a new concept, should students engage in problem solving followed by instruction (PS-I) or instruction followed by problem solving (I-PS)? Noting that there is a passionate debate about the design of initial learning, we report evidence from a meta-analysis of 53 studies with 166 comparisons that compared PS-I with I-PS design. Our results showed a significant, moderate effect in favor of PS-I (Hedge's g 0.36 [95% confidence interval 0.20; 0.51]). The effects were even stronger (Hedge's g ranging between 0.37 and 0.58) when PS-I was implemented with high fidelity to the principles of Productive Failure (PF), a subset variant of PS-I design. Students' grade level, intervention time span, and its (quasi-)experimental nature contributed to the efficacy of PS-I over I-PS designs. Contrasting trends were, however, observed for younger age learners (second to fifth graders) and for the learning of domain-general skills, for which effect sizes favored I-PS. Overall, an estimation of true effect sizes after accounting for publication bias suggested a strong effect size favoring PS-I (Hedge's g 0.87)."

If you managed to follow all of that, you might wish to seek out the full paper, which is easily found on-line and is freely available. But what's this got to do with our game of checkers?

As it turns out, quite a bit. Should we study a concept in a checker book (like, for instance, fourth position) and then solve problems based on that theme? Or should we try some problems first, likely encountering failure, and only then go back and study the tutorial material? The paper suggests the latter for all but the youngest age groups.

Well, then, let's put this into practice, shall we? Here's a problem from Richard Pask's best-selling (in checker book terms, at least) Checkers for the Novice. If you're an expert player, you'll find the problem easy and you won't need the instruction. But for the rest of us --- what learning method will work best?

Choose your approach. See what resonates with you. You can actually experiment with the entire book, if you wish.

We won't give the solution here; it's Diagram 57, part of Lesson 11 in Mr. Pask's book. If by any chance you don't have a copy, it's a free download.

So, what method did you choose? What was the easiest way for you to learn the concept demonstrated in this problem? Book first? Problem first? Do let us know what you think.

Although this column is being written some weeks in advance, it looks as though 4th of July 2022 is going to be a vast improvement over the past Covid years. Although we know that Covid will never be completely gone, we're back to at least some semblance of normal, and there will be 4th of July parades and outdoor celebrations. And while the world situation and the economy could be better, we're happy for what we have, and most of all we're happy and proud to be Americans and we love celebrating the anniversary of our nation's independence.

On such holidays we often turn to another American patriot, the great champion Tommie Wiswell. Today we have a problem he called Blitz, and you'll see why when you solve it.

See if you can win it. You don't have to play "blitz" --- take all the time you want, but when you're finished, definitely blitz your mouse over to Read More to see the solution.

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There's an interesting book titled A Theory of Fun for Game Design by Raph Koster, published in 2004. The book touches on some valid points about how games are designed and ultimately played. However, when it comes to our game of checkers, Mr. Koster says the following.

"Until now, I've been discussing formal game design--- abstract simulations. But we reely see truly abstract simulations in games. People tend to dress up game systems with some fiction. Designers put artwork on them that is suggestive of some real-world context. Take checkers for example--- abstractly it's a board game about entrapment and forced action, played on a diamond-shaped grid. When we say "king me" in checkers, we're adding a subtle bit of fiction to the game; suddenly it has acquired feudal overtones and a medieval context. Usually, the pieces have a crown embossed on them."

We don't have enough space in this column to discuss all of Mr. Koster's errors and misconceptions; suffice it to say that he seems to have little or no knowledge of checkers played as a serious game. However, we did get genuine amusement from the idea of "feudal overtones" related to the process of crowning a piece. We wonder if, as a potential player, he would also subscribe to the common erroneous advice to "always keep your king-row intact."

So, for today's checker problem, let's use our collective imagination. Think of the kings as bearing jeweled crowns and dressed in the finest of purple robes. Think of the men as clad in leather armor and metal helmets, bearing swords, axes, and pikes. Think of the checkerboard as the field of battle, perhaps in ancient Carthage (ancient rather than medieval, but still quite colorful). Listen to the call of trumpets, the beat of drums, the battle cries of the massed warriors.

Or maybe not. Perhaps you'd just like to solve a good checker problem without a lot of distracting imagery. It's up to you. Was Mr. Koster correct or incorrect with his medieval contexts and feudal overtones? Does it really matter?

See how you do with this one and then click on (or march over to, if you will) Read More to view the solution.

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In May, Marvin J. Mavin had once again led the Detroit Doublejumpers to another World Series of Checkers Championship, defeating the Los Angeles Leapers over the course of seven hard-fought matches.

June and July were off months; training camp didn't take place until August. Marvin and his financee, Priscilla, usually took separate vacations in June and a vacation together in July.

This year Marvin decided to go to Maine. It would be just about the start of the height of the lobster season, and there would also be fresh fish caught in cold Atlantic waters, of course with a nice crisp beer (or two) as an accompaniment.

It was quite a drive from Detroit to Lubeck, Maine, especially in Marvin's very old Volkswagen Beetle. He took his time and after two overnight stays, checked into Cohill's Inn, a well-known pub with several rustic rooms to rent.

Marvin spent a day or two exploring the town, trying to remain incognito, as even remote Lubeck had its checker fans, and the town had an amateur team appropriately named the Lubeck Lobsters, who competed in a league in eastern Maine.

Of course, a star such as Marvin couldn't help but eventually be noticed. However, though Maine folk are very friendly, they do respect a person's privacy, so Marvin didn't have to do a lot more than sign a few autographs, shake a few hands, and pose for some selfies.

About a week into his visit, Marvin was enjoying some local brews in the Lubeck Tavern. He had gotten to talking with a few of the lobster fisherman and raised a couple of glasses with them. Well, maybe more than just a couple. But fishermen rise early and by about 11 o'clock the tavern was empty except for Marvin and the bartender. Closing time wasn't until one AM but the bartender looked tired so Marvin called for one last beer before going back to his lodgings.

He must have taken his time with his beer, for as he drained the last of it he looked up at the tavern's old grandfather clock and saw that it was exactly midnight. He was going to get up to leave but all of a sudden he noticed a large, middle-aged, ruddy-looking man sitting opposite him at his table.

"Where did you come from?" Marvin said, startled by the man's sudden appearance.

"Where did I come from?" the man replied in a voice that was shaky and distant. "What do you mean, where did I come from! Don't you know me? Everybody around here knows The Great Murray! John Murray, that's me, and they call me The Great Murray because of how well I play checkers. The best in Eastern Maine. Maybe the best in all of Maine. Might even be the best in the world only haven't quite got the title yet."

"But," he continued, "I'm going to get there, and I'll start by beating you. Yes, you're some kind of hot-shot professional but I'm not scared, no sir I am not, because you're nothing compared to The Great Murray."

Suddenly there was a rustic old checkerboard on the table. Murray set it up and quickly made a move with the Black pieces. "Now there, your turn, so play."

Marvin, still startled, replied, "Hey, look, whoever you are, it's kinda late and I've had a couple of ... well a few ... quite a few ... anyhow I want to get to bed, so look, why don'tcha come back another night."

"Play, I said!" Murray banged a fist on the table. "Play if you'd like to get to bed in one piece tonight!"

"Aw, c'mon now ... "

Now the fist was inches from Marvin's face. Marvin looked over at the bar, but the bartender was nowhere to be seen.

A sudden shiver went through Marvin's body. Without even meaning to, he reached out his hand and made a move.

The game went on, Murray glowering all the time. Once or twice Marvin made as if to get up and leave, and on each occasion Murray said, "You may not leave unless you resign the game!"

Eventually the play led to the following position.

"Ha ha ha," Murray laughed, "you shall lose now. And you know what shall happen then? I will spread the word far and wide that The Great Murray beat this so-called professional champion, and you shall see if any pro team wants you after that. You shall die poor lying in the gutter because tonight is when your career ends."

Marvin heard these words, stunned. But something must have gotten through to him, because all at once, he sat up straight and said, "Now wait a minute there pal, just who do you think you are? Great Murray? You ain't great anything, 'cept maybe a Great Windbag! Now take this, you old blowhard!"

Marvin looked down at the checkerboard and made his move.

---

Is The Great Murray all that great? Is he the equal of Marvin J. Mavin? Are you up to Murray's challenge? See how you do with the position above and then click on Read More to see the solution and the conclusion to our story.

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Bad Teacher was a terrible film from the year 2011. We certainly don't recommend it, but the idea does lead us nicely into today's Checker Maven column.

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LARNER TRIES TO TEACH

"This is the way," said Larner impatiently as he persisted in rapidly solving a problem without giving the boastful Skittle a trial.

Galileo once said, "You cannot teach a man anything; you can only help him to find it within himself." How could Skittle learn without being permitted to make mistakes and then correct them?

Since 1775, due largely to the experiments of Johann Pestalozzi, the science of education has been based on problem solving or reasoning, rather than on memorizing. This Swiss educationalist combined manual with mental exercises. Teachers merely develop your latent power. You learn mainly by practice!

---

The preceding short selection is from Andrew J. Banks' eclectic book, Checker Board Strategy. It seems that Mr. Larner, whoever he was, is an example of a bad teacher. Is it true, for our game of checkers, that we learn mainly by practice, and that teachers merely develop our latent power?

That could be the subject of an extended and interesting debate. But for the moment, let's get some practice, with today's rather easy problem. It's really at the beginner level but more experienced players should see if they can solve it with just a quick glance.

Did you solve it rapidly? Did it provide any sort of useful practice? We surely don't have to teach you that you can click on Read More to verify your solution.

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It's the month of June and in some parts of North America it's the "June Bug" season. The June Bug is related to the scarab, and there are some 100 varieties of this insect. It makes a brief appearance usually in May and June each year, hence the name "June Bug" (or sometimes "May Bug"). They are widely considered to be a pest harmful to trees and lawn.

What's that got to do with checkers, and our (more or less) monthly speed problem? Take a look at the diagram below.

So, you say, it's pretty straightforward, right? What's the point of a problem with such an "obvious" solution? Well, then--- this one could indeed "bug" you if you get it wrong. Experienced players won't have any difficulty. But the rest of us might, shall we say, get, um, bitten[1].

Solve it quickly and then let your mouse crawl over to Read More to see the solution.

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[1] June bugs don't actually bite humans, but allow us this small artistic liberty.

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Many years ago, when checkers was played by man and by man alone, for there were no computers nor would there be for almost two centuries, a legendary person created a 9x9 checker problem that challenged the best players of the day; and yet they solved the problem despite its depth, trickery, and unusual nature. The creator of the problem was said to be named Hink, or perhaps it was The Hink, or perhaps it was someone else, for no one really knew, and yet the problem was known as Hink's Problem.

Down through the ensuing generations, Hink's Problem entertained and baffled, yet still, the best in each generation would solve it with enough thought and reflection.

And then came the time of the computers.

The earliest, created by a researcher at a large corporation, did not play checkers very well and of course could not solve Hink's Problem.

More computers arrived and more checker engines were created, and though they bore names like Fiend and Giant and Mountain Wind, and even Crowning Touch and Cookie--- the latter two being the greatest of their day--- still they could not solve Hink's Problem while the masters and grandmasters, all of them fully human, were able to succeed.

And so arose the Checker Question: Would, one day, computers solve Hink's problem?

More time passed and more generations came and went, and computers became universal, and beyond the comprehension of man, so incredible was their power. Men no longer designed new computers; the computers themselves did that until they became seemingly omnipotent. Yet still, they could not solve Hink's problem, while human masters--- the few that there still were--- would do so.

Millennia turned into millions of years and millions of years turned to billions, and the computers merged into one great Omnicomputer that integrated with the very fabric of the universe. But Hink's Problem remained beyond them. There were no humans left to solve it, for they had all moved into a higher plane of existence, but had there been any, they would surely have found the solution.

Finally, the universe began to darken. The Omnicomputer had long known that the omega constant was less than one and the universe would eventually face heat death.

The last star winked out, and still Hink's Problem was beyond the Omnicomputer. It was the last unsolved problem that the great engine faced, and it could not shut down until the solution was found.

Finally, after so long that time no longer had any meaning, the Omnicomputer said, "It cannot be done" and this so upset the Omnicomputer that it erupted from its containment in the hyperdimensions, creating a New Big Bang that would give rise to a new universe, perhaps one in which the laws of logic would differ enough for Hink's Problem to be solvable, not just by humans, but by a mere Omnicomputer.

With apologies to Isaac Asimov, whose classic The Last Question inspired this story,

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The Omnicomputer couldn't solve this one and had the cyber equivalent of a nervous breakdown. Can you solve it? It's probably at grandmaster level, but it's fascinating and worth your time. Just don't get so upset that you explode! After all you can always give your mouse a big bang on Read More to see the solution.

[Read More]

It was the last Saturday in May of 1955. In Bismarck, North Dakota, that meant the last frost of the winter was probably in the books, yards had been raked up and readied for the summer weeks ago, and outdoor life was stirring. Some flowers had started to bloom and in a couple of weeks Sal Westerman would have fresh asparagus from his garden, and fresh strawberries, too.

But it also meant that this would be the final meeting of Sal's beloved Coffee and Cake Checker Club before they took their summer break, which lasted from Memorial Day until Labor Day. Their meeting place, the Beacon Cafe, was closed on summer Saturdays, and during the whole month of August when the owner, Deana Nagel, went to Gackle to spend time on her family farm and help with the harvest.

The sun was out and the temperature was around 70 degrees when Sal walked the few blocks from his modest home to the Provident Life Building, where the Cafe was located. He expected a good turnout, as was usually the case for the last meeting of the season, and when he walked in the door he wasn't disappointed. Nearly everyone was there: Larry, Wayne, Delmer, Spooler, Louie the Flash, Ron, Tom, Dan, and even Ted, Howie, and Frank, the latter three being only infrequent participants. The group took up three booths in the back, and Deana was all smiles. Business was going to be good today.

"Rhubarb bars," she announced, "and I've got lots of them!"

It was a long-standing tradition that Sal would bring along a checker problem, and if the "boys" (all of them at least 50 years old) could solve it, Sal would buy the treats, but if they couldn't, Sal got treated by them. Sal always made sure he brought along a tough problem to even the odds a little.

The boys talked for a little while, drinking coffee and playing a few informal games. Many of them had summer vacation plans, generally involving time on their farms (now usually run by their children), or visits to relatives around and about North Dakota, South Dakota, and Montana. Ron and his wife were actually going on a cruise; they'd take the train to New York and then sail for Paris. That was pretty unusual for most folk in Bismarck, who didn't feel comfortable when they were very far from home.

At around 2 o'clock the boys started clamoring for Sal to show his problem. "Gettin' kind of hungry in here," Wayne remarked. "Must be time for Sal to be buying us some of those rhubarb bars."

Sal smiled. "We'll see about that," he said, "I've got one from Ed and it's going to get published in All Checkers Digest."

The expression on Wayne's face changed. Ed, who was from Pennsylvania and one of Sal's checker pen-pals, always came up with tough, clever problems, and if All Checkers Digest was going to print it, then it must be really something.

Sal laid out the following position on several of the checkerboards. "Okay boys," he said, "let's see what you can do with this one!"

"Oh ... " Louie the Flash said.

"Oh my ... " Howie said.

"Yikes!" Larry said.

Deana brought over more coffee as the boys set to work.

---

Fortunately, The Checker Maven doesn't take the summer off. But neither do we serve rhubarb bars, so you're on your own for afternoon treats. But do try to solve the problem and then click on Read More to see the solution and the conclusion of our little story.

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Today we won't go into the difference between breeches and britches, but we will mention that breeches are pants (or if you like, pantaloons) that cover the, um, posterior. Today that's true of most if not all pants.

What then, are double breeches? In terms of pants, we can't really say, but our Research Department did point out that the word breeches is what's known as a double plural. In old English, broc was a word which had a plural form of brec. In time the word evolved and added the usual -(e)s suffix and thus became the double plural, breeches.

If that's just a bit too complicated, fortunately in checkers double breeches has a very specific and easy to understand meaning, as you'll see in Bill Salot's 62nd World Championship Problem Composing Contest, which has double breeches as its theme. Access the contest problems here.

To get you started, here's a sample problem illustrating the contest theme. It's by grandmaster composer Ed Atkinson and was the winner of Contest 33 in June, 2017.

After you've enjoyed solving this problem, click on Read More to see the solution, and then go to the contest page to cast your vote for your favorite among four additional problems.

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