In our modern day, a certain Jack Barker has written a book about "The Conjoined Triangles of Success" which supposedly will guide you to running a startup company that thrives. Engineering and Manufacturing meet Sales and Growth along the hypotenuse of Compromise.

We can't really speak to this methodology, but there is another Barker and another triangle that predates the modern interpretation by over 100 years. It's a study by the famed checkerist C. F. Barker, and his position, shown below, is often known as Barker's Triangle.

We've got to say this problem is one of the most instructive we've ever come across. Why it's called a 'triangle' will become clear when you find the solution. So, give it a good effort and then triangulate your mouse on Read More to see how it's done.

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The holidays were over and now North Dakota was in the depths of winter. With even daytime temperatures often well below zero and plenty of snowy days, residents of Bismarck tended to spend as little time out of doors as possible.

Sal had arrived early at the Beacon Cafe for the regular Saturday afternoon session of the Coffee and Cake Checker Club, and he was warming himself with a steaming hot cup of Deana's coffee. Deana, the proprietor, made good coffee and even better desserts, surely the best for miles around.

The boys--- that's what Sal called the other members of the club, even though they were all over fifty--- were still stinging a little from the beating they took when Sal challenged them, just before the holidays, with his friend Brian's 6x6. Sal chuckled to himself. They were going to get another surprise today.

The boys started to file in out of the cold, all of them wearing winter parkas, wool caps, heavy gloves, and fur-lined boots. One by one they joined Sal at the big booth in the back. Wayne, Louie, Larry, and Delmer were there, and to everyone's surprise, so was Kevin, who only showed up a couple of times a year.

"Hey Spooler, seeing you're here for a change, you buying today?" Wayne asked. Kevin went by the nickname Spooler for reasons not really known to anyone.

"Buying what?" Kevin asked innocently.

"Caramel rolls," Deana called over from behind her counter. "Just baked a fresh tray of them. Great with coffee, especially on a day like this." Deana was, among many other things, a great promoter of her wares.

Everyone looked at Sal. "Okay, what've you got?" Larry asked. "Make it a good one so Spooler can buy for everyone."

"Just so happens," Sal said, "there's one from Ed that he calls 'Code Breaker.'" Ed, from Pennsylvania, was Sal's other checker penpal.

"Is it as hard as that one from Brian last month?" Delmer asked.

"See for yourself," Sal said, as he set up the following position on his favorite checkerboard.

"Oh, that doesn't look too ..." Spooler began, but then he stopped. "Uh ... wait a minute ..."

Everyone laughed. But only for a moment, for they were all soon busy examining the checkerboard.

"Fifteen minutes I'll give you," Sal said, but the concentration was so deep his words went unheard.

"Time's up," Sal said a quarter of an hour later.

"I've got it," Larry said. "Let me show you. It's just like ..."

"NO!" Wayne, Delmer, and Louie shouted all at once. "We want Spooler to pay today," Delmer pointed out.

"Aw, c'mon guys, I don't know how to do it," Spooler said. "You just want me to pay because I don't come every week.

Heads nodded in unison. "Not even every month," Wayne pointed out.

"But, okay," Spooler said. "I'll buy ... if Larry really has it right."

---

This really fine problem by master problemist Ed Atkinson is challenging but solvable, and the promise of one of Deana's caramel rolls would be too much for anyone to resist. Can you solve it? We urge you to give it a good trial. Now, we don't know if anything like The Beacon Cafe is in your area, but coffee and cake are certainly in order if you make a genuine effort. When you're ready, click on Read More for the solution and the rest of the story.

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The New Year 2020 is here and we've already been subject to all too many jokes about 2020 vision and so on. So let's skip all that and, while wishing all our readers the best of the New Year, we'll jump right into a nice little speed problem sent by regular contributors Lloyd and Josh Gordon. We won't use our Javascript clock this month. The problem isn't at all difficult but we thought we'd give you a chance to "ease" into the New Year.

Black is a piece up but White is about to even the count. How can Black win?

Even if you're still feeling the results of your New Year's Eve party, you can solve this one. Find the solution and then click on Read More to check your work.

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Priscilla Snelson, Chief Operating Officer for the international conglomerate Rust Belt Holdings in Detroit, was putting on an exclusive New Year's Eve party at her upscale condo in the swanky suburb where she resided.

The party was what you would expect from someone of her business standing. Only top executives and wealthy friends were invited. The food was catered from a company run by a three-star Michelin chef. The music came from Priscilla's ten thousand dollar custom audio system.

Of course, Marvin J. Mavin, Priscilla's long-time boyfriend--- although she referred to him as her "beau"--- was there. Not exactly by invitation; high end parties weren't his thing. More by fiat. Priscilla had told him that he was to be there or else, and that was the end of the discussion.

Everyone was circulating around the huge living room and kitchen, drinks in hand, making small chitchat.

Marvin was bored out of his mind. As Captain of the Detroit Doublejumpers, one of the top teams in the National Checker League, his interests definitely didn't run to the price of scrap tin in Kurdistan or the molybdenum futures market.

No, Marvin liked a good beer or two. Or more. And this party was definitely one of those "more" occasions.

So, at some point into the evening, Marvin was on perhaps his fifth beer--- he had lost track of the exact count--- and he was starting to feel pretty loose and relaxed.

At that moment Priscilla, who until now had been far too busy with her guests to pay much attention to Marvin, came over to where he was standing, a young girl in tow.

"Marv," she said, "I'd like you to meet ..." Priscilla stopped in mid-sentence when she saw that Marvin was in a somewhat zozzled state.

"Oh, dear," she said, "maybe another time."

"Oh, no, no, Auntie Prissy!" the little girl piped up. "I want to meet Captain Marvin! He's my hero! Some day I'm going to grow up to be a checker star just like him!"

"Another time, dear," Priscilla said, but Marvin interjected, "Yeah, Prissy! She wants to meet her hero! Ain'tcha gonna let her?"

Priscilla scowled, but she knew she was trapped. "Very well, then," she said, "Marvin, this is Harriet Liang. She plays for her grade school checker team over in Dearborn, and she's very good."

Marvin leaned down to shake hands. "Nice to meet ya," he said, his voice a bit slurred.

"Auntie Prissy, why is Captain Marvin talking so funny?" Harriet asked.

"Oh, it's just because ... well, never mind that," Priscilla said. "Now, why don't you show Uncle Marvin your problem."

Harriet beamed, "Oh wow, yes!" She pulled a sheet of paper from the pocket of her dress. "Here, Captain Marvin. It's a checker problem, and my Uncle Brian said to try it out on you!"

Marvin looked at the diagram and then looked puzzled. "Hey, what's a little kid like you doing at an adult party ..."

"Her Uncle Brian, from St. Louis, is working on a major deal with us, and he asked me if I would introduce his niece to you."

"I see," Marvin said. "The old you scratch my back I scratch yours routine, hey?" He reached for Priscilla's arm but she stepped back away.

"Okay, okay." Marvin turned to Harriet. "Well, let's see now, this should be easy, you just ... hmm, no, I guess you don't. Suppose you ... nope, doesn't work either."

"Captain Marvin, I solved in four minutes and my coach told me I was very smart!" Harriet said.

Marvin now regretted having those last couple of beers. If only he could think straight! Then Priscilla, as if she had read his mind, said, "I hope you learn something from this. Come on, Harriet, let's get you a soda and a snack. I think Captain Marvin is going to need a while."

---

It's pretty clear that drinking too much didn't lead to a good outcome; after all, it never does. Can you keep a clear head and solve the checker problem that Marvin, in his "zozzled" state, couldn't handle? Little Harriet won praise for her rapid solution. How well can you do?

Try it out and then click on Read More to see the solution and the conclusion of our story.

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Four-In-A-Row, sometimes called "Connect Four" is a strategy board game that is actually quite good. Shown above is a large outdoor game set that you can buy for your backyard for only ... um ... $300.00 plus shipping.

At The Checker Maven, though, our game is checkers, and nothing will cost you $300.00 (or anything at all, as our content is completely free). However, our theme for this column is indeed "Four In A Row."

In today's Checker School entry, we're trying something a little different. When you click on the link below, you'll be presented with not one, not two, nor even three, but four elementary checker problems. Your job? Solve them as quickly as possible, and our Javascript clock will "help" you keep track of your time. Can you solve four in a row?

A top player won't require more than a minute or two, which includes time to read the problem terms and look at the diagrams. Those of us with lesser skills will require more time, of course, and perhaps quite a bit more.

But no matter; do the best you can. Are you ready?

Click to display problems

When you're done, click the "back" button on your browser and then Read More to check your solutions, all in a row.

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It was September and the Coffee and Cake Checker Club was meeting for the first time after the usual summer hiatus. There was a good turnout this week with Sal and five of the boys present: Wayne, Delmer, Louie, Dan, and Mike. The "boys" were all over 50 years old, but nevertheless that's how Sal Westerman, the club's leader, thought of them.

Sal should have been happy. He loved these Saturday afternoon gatherings at The Beacon Cafe more than just about anything else. It was September, 1955, and the weather in Bismarck, North Dakota had started to turn cooler.

So it might surprise you to hear that Sal wasn't the least bit happy.

It all started when Deana, the proprietor of the Beacon Cafe in Bismarck, North Dakota announced that she had fresh lemon bars this afternoon, and Sal frowned. More like scowled, because Sal didn't like lemon bars, not one little bit. He just plain didn't like them, no matter how good they were.

"Lemon bars, Sal!" Dan Kemper, one of the boys, said in a teasing tone. "Don't you want to win one?"

"No, I do not," Sal said emphatically. He looked over to Deana's service counter. "Deana, don't you have anything else?" he asked her.

"Got some fudge brownies left over from yesterday," she said. "Half price for day-old. But the lemon bars are fresh and good." She frowned in turn. Sal had been coming to the Beacon for so long she knew exactly what he liked and didn't like, but she always felt a little insulted when her customers didn't care for her baked products. Everyone said she had the best desserts in town. Even Mayor Lips came here often for coffee and treats with his political pals.

Dan continued, "Come on, Sal, I know you've got a coffee and cake problem for us. Heck, you don't have to eat lemon bars if you don't want to--- more for us!" Dan said, and the rest of the boys added their agreement.

"Okay, okay," Sal said, "it just happens that Ed sent me a nice one." Ed was Sal's checker pen pal in Pennsylvania. "Guess I'll have to settle for those day-old brownies when you boys can't solve it."

They all laughed. "Hey, how about if we do solve it you have to eat a lemon bar?" Dan suggested.

"That's not even funny," Sal replied.

Deana wasn't laughing, either. "You make fun of my food, you leave," she threatened. Deana didn't get upset very often but when she did, you had better watch out.

Sal realized that things were going into the ditch in a hurry. "Okay, okay!" he said. "Let there be peace! I'll show you Ed's problem, and whether you solve it or not, I'll buy lemon bars for everyone and a brownie for myself! How's that sound?"

Everyone now smiled, even Deana. The tension was relieved and Sal set out the following position on one of the checkerboards in the big booth that the club always occupied.

"Ed calls this one Sweet Spot," Sal said. "What do you boys think?"

Five minutes passed with everyone scratching their heads and looking puzzled. "Five more minutes," Sal announced.

---

Can you win this one? And what's your take on lemon bars? (Be careful what you say; Deana might hear you.) When you've given this one a good try, click on Read More to see the solution and the conclusion of today's story.

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The Cakewalk goes back a long way, and is intimately connected with Black history and pre-Civil War southern plantation life. But today, a Cakewalk is something of a carnival game, something like musical chairs but with a cake as the prize. The word has also come to mean something that is extremely easy to do or accomplish.

And no, today's column doesn't have anything to do with our ongoing Coffee and Cake series; we've chosen the title Cakewalk because today's problem is very easy indeed. It's so easy that we've resurrected our long-neglected Javascript timer.

Expert players will take longer to read the terms of the problem than they will to solve it; an instant solution is likely. Even intermediates will solve it just about at once. Beginners may have to reflect a few seconds but they too should not have much trouble.

Why such an easy problem? Well, we present hard ones week after week and once in a while we think it's good to go in the other direction. Players of all levels should find a home in our columns. The position was sent to us by regular contributors Lloyd and Josh Gordon of Toronto and arose over the board.

So here we go. Click below to show the problem and start the clock.

Cakewalk (very easy)

Got it? Of course you did. But click on Read More all the same, just to be sure.

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Hogan's Heros was an American television program that ran from 1965 through 1971. It was pretty popular in its time, although today's politically correct, looking-to-be-offended crowd would find it unacceptable.

But there was a different and earlier Hogan, namely E. W. Hogan of Emo, Ontario, who is a hero to us in a checker sort of way. Some time in the latter part of the 1930s he published a problem that to this day is a bit resistant to computer solution. Take a look at the diagram below.

Yes, the KingsRow computer engine found the solution ... but it did have to think about it for a few seconds (normally KingsRow solves positions virtually instantaneously).

So we think you'll find it to be an interesting challenge. Don't worry about being politically correct; become one of E. W. Hogan's heros and try to solve it. When you're ready, click on Read More to see the solution.

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Uh-oh. Someone is in deep trouble. That fellow is going to have to work very hard and very quickly to find a draw and avoid a loss, so to speak.

Of course, things like this come up in checkers all the time. We make a move and then wish we had made another. Sometimes the draw is still there, and sometimes not. Take a look at the position below.

White has just played 6-9. It looks logical at first glance, doesn't it? Actually, the move is sound if maybe not optimal, but as usual, playing it out over the board is the real issue. This quick little study is based on a position sent to us by regular contributors Josh and Lloyd Gordon of Toronto. It's not quite a speed problem, but it isn't too hard if you keep your wits about you.

Stay out of trouble; solve the problem and be able to say the much more positive phrase, "I did it!" You can always click on Read More to check your solution.

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Shown above is what is now a pub called The Clock Warehouse in Shardlow, Derbyshire, England. The pub is said to be dog-friendly. We're not quite sure what that means. We would rather have heard that the pub was checker (draughts) friendly.

Today, we consider a problem by a checkerist named Shardlow who didn't come from England, but from Marshall, Minnesota. What was his connection, if any, with the town in England? Most likely there is none, though we'll probably never know.

Mr. F. C. Shardlow published a number of problems in various newspapers; the one below appeared in The Winnipeg Free Press in 1938. All we were able to turn up about the author was that his full name was Frederick Cromwell Shardlow, that he was born in 1874, passed on in 1948, and had a wife and two daughters. We didn't find anything additional about his checker career, although he obviously must have been quite good.

A checker friendly problem? We think so. Try to solve it, and then give a friendly click of the mouse on Read More to see the solution.

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