When voting you have to make a choice. It's often (though not always) between two viable candidates. There are of course endless situations in life that require making a choice. Sometimes there are many options, some times just one or two. We make choices in checkers, too, among various possible moves. This column has the title "Tinsley's Choice" for reasons that will soon become apparent.

Today's problem derives from a position that occurred in the 1956 U.S. National tournament in a game played by the great Marion Tinsley against one A. Cameron. You won't be surprised to hear that Dr. Tinsley won the game, but you may be surprised at just how he won. First let's look at the run-up to the critical position.

1.	9-14	24-19
2.	11-15	22-18
3.	15x24	18x9
4.	5x14	28x19
5.	8-11	25-22
6.	11-15	32-28
7.	15x24	28x19
8.	7-11	22-18
9.	1-5	18x9
10.	5x14	29-25
11.	4-8	25-22
12.	11-15	22-18
13.	15x24	27x20
14.	6-9	26-22
15.	8-11	30-26
16.	10-15	22-17
17.	15x22	17x10
18.	22-25	23-18

Loses. 10-6 would hold the draw.

19.	25-30	26-23
20.	9-13	18-14
21.	30-25	14-9
22.	25-22	9-5
23.	22-25	5-1
24.	2-6	10-7
25.	3x10	1-5

At this juncture you might or might not be surprised to hear that there are just two Black moves which lead to a win (if we told you why we'd give too much away). We would of course expect Black, being a piece up, to have the win. However one move leads to a longer win while another move leads to a snappy finish. Which one do you think Dr. Tinsley played? Can you find both of them and show the winning lines of play?

The answers may surprise you. See how you do and then click on Read More to see the solutions and to find out what actually happened over the board.

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It was April and the common saying about "April showers" had taken on a new meaning for Marvin J. Mavin and the Detroit Doublejumpers of the National Checker League.

The Doublejumpers were in Portland, where the old Portland Playpen Arena was still in service for the matches of the Portland Pitchers. The Arena was showing its age. Seating capacity had been reduced about 25% during bad weather because of leaks in the dome roof. The playing field itself had numerous wet spots, and play would have to take place not in the center of the field, but off to one side where the pitch remained dry.

Of course the fans were not happy and neither was team management, who saw declining ticket sales and revenue. Portland has a lot of rainy weather and it was becoming quite a problem.

Portland city government promised to build a new stadium in order to keep the team from moving to another city. Tucson, Arizona, had made an offer and pointed out that there weren't rainy weather problems or even leaky roofs to worry about. Of course Portland had promised a new stadium for a couple of years and allowed as how they could surely get it built in less than 20 more years--- or maybe a little longer than that; they didn't really know.

The irony was that Portland had been playing quite well this season and would likely make the playoffs, which were just about a month away. But fans just didn't want to come out and sit on wet seats and have a non-optimal view.

So it came about that in the first match of a three-match series, the weather was bad even by Portland standards and attendance was only about 8,000 in a stadium that was supposed to seat 50,000. But the show must go on, and on first board Marvin met up with an old foe, D. Rock Noodle, who had played first board for the Pitchers for quite a little while. Ever since they had first met, Marvin had been avoiding D. Rock's crusher handshakes, despite D. Rock's taunting.

The roof leaks were pretty bad on such a rainy day and the playing area had been set up in a slightly less wet area along what would have been the foul line in left field in a baseball stadium. Even there, the ground was slightly wet and the grounds crew had put down a tarp. Stadium management thought of erecting a tent roof over the area but that was finally vetoed as it would restrict the view of the fans even more. There was always the option of moving the match indoors to one of the conference areas but that would mean issuing full refunds plus additional vouchers as compensation to all ticket holders and management couldn't bear the expense.

The starting whistle blew and the call "Play Checkers!" rang out. The teams were surprisingly closely matched. Boards 2 through 4 produced draws; board 5 was a Doublejumper win, leading to a score of 2.5 to 1.5 in favor of Detroit. Everything was now up to Marvin and D. Rock on board 1. If Marvin could draw, the score would end at 3-2, giving the Doublejumpers the win. However if Marvin lost, the score would be 2.5-2.5, and since tie-breaks went from highest board to lowest, the loss on board 1 would give the match to the Pitchers.

The game reached a very tense position with Marvin to play. Both players were short on time, even with the 40 moves in two hours time control, and it looked like things could go either way.

Marvin, though, had an idea. With just under a minute left on the clock, Marvin reached out ...

There was a loud crack high overhead in the stadium dome roof, and all at once a torrent of water poured down directly on board 1! Both Marvin and D. Rock were knocked from their chairs and the board swept off the table.

Marvin and D. Rock picked themselves up. Both of them were soaked through, and rain continued to pour down through the new, large hole in the roof.

The referee, Willy Will Wilson, blew his whistle. "Game over!" he called out. "Win for Black!"

"Hey, ref, wait a minute," Marvin said, all the while trying to shake off some of the water from his arms, legs, and head, "I was going to make my move and draw the game. How do you get a win for Black here?"

D. Rock laughed. "Sorry, pal," he said. "The ref knows the rules. Game adjourned. And since we passed the four hour mark, Rule 3.1415926 says in time scramble situations, disruption of the board results in a loss for the player on move. You lose, fella."

"The rule was quoted correctly," said Willy Will. "After four hours the board is not reset. Player on move loses. Black wins." He blew his whistle again for good measure.

Within seconds the Doublejumper coach, Baba Dudut (who had replaced Davey Anderson after the controversial events we recounted in last fall's stories), was on the field, confronting the referee. "Just a minute there!" Baba said. "We didn't reach four hours. Look at the clocks. We're still in the first time control. Marvin had 48 seconds left and D. Rock had 54 seconds. And besides, upsetting the board was an act of nature, not deliberately done by my player!"

Baba Dudut reached down and pulled the game timer out of the sodden mess that the pitch had become. But the clock was completely filled with mud. "Oh ... well never mind, look at the stadium clock!" he told Willy Will.

"Stadium clocks are unofficial," Willy Will said, "and rule 3.1415926 doesn't take into account deliberate or non-deliberate board upsets. Do I need to blow my whistle again? Black wins and Portland wins. Clear the field, everyone. Go change into dry clothes."

"I'll appeal!" said Baba. "You'll regret this! You should have let us finish the match indoors!"

Willy Will did not reply, and Marvin looked as if he was about to speak, but Baba turned to him and said, "Not a word from you! You'll just say something dumb and make things worse!"

Meanwhile D. Rock continued to laugh and the few fans that were still in the stadium, all of them Pitcher fans, were hooting and hollering.

Willy Will blew his whistle one last time and ordered everyone off the field, making threats of fines and suspensions.

"Oh, go blow your horn!" Baba said in disgust as he took Marvin by the elbow and led him to the dugout exit.

"Coach, I coulda ... " Marvin began but Baba cut him off. "I don't want to hear it! Coulda, shoulda, well, you shoulda been faster and made your move before the roof cracked! You haven't heard the last of this!"

Marvin shrugged his shoulders. "Gee, how was I supposed to know that the roof ... "

"A player should always be aware!" Baba snapped. "No matter what!"

To be continued.

---

We'd say Marvin is in hot water again but the rainwater that soaked him was probably pretty cold. Did Marvin have a draw on the board before the "April showers" ended the match? (Do you think rule 3.1415926 is fair?) See what you can work out and then click on Read More to get the answer.

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It was Saturday, April 9, 1955, the day before Easter Sunday. It was the regularly scheduled meeting day of Bismarck, North Dakota's Coffee and Cake Checker Club, informally led by the respected elderly gentleman Sal Westerman. The club met every Saturday from just after Labor Day until just before Memorial Day, with a brief break for Thanksgiving, Christmas, and New Year's.

But today there was a problem.

The club invariably met at the Beacon Cafe, a popular local spot run by championship baker Deana Nagel. Saturday afternoons post-lunch were typically slow and Deana welcomed the Club and was friends with all of the "boys" (all but one of whom were over 50 years of age). However, this year Deana closed up for the Easter weekend. It was something she hadn't done in prior years but this year, she wanted to spend the weekend in Gackle, North Dakota, where her aging grandmother had come from Iowa for a rather rare visit.

Of course Sal could hardly blame Deana; certainly she should visit with her grandmother. But that left open the question of what to do about the club. The "boys" had discussed it the prior week and didn't come up with much in the way of a solution. The public library was a possible option but coffee and treats were not permitted on premises. There were other cafes and coffee shops but the boys were used to meeting at the Beacon.

"We could go to Bob's Big Boy," Delmer had suggested the previous week. Big Boy had just opened the prior year and was a popular spot. But Wayne pointed out that they didn't have indoor seating. A couple of other options were reviewed. The general feeling was not to go to a bar or a hotel lounge, and restaurants tended to be too busy.

It must have been Louie the Flash who suggested gathering at Sal's home.

"Oh, I don't know," Sal had said, "I'd have to ask Sylvia." Sylvia was Sal's wife of many decades. "And our house is pretty small."

"Hey, I've visited you and your basement is set up for checkers," Dan said. "We can all squeeze in, and we can go pot luck on bringing the treats."

Sal said he would think about it and that evening he asked Sylvia, who agreed, if a bit relucantly. "Whatever makes you happy, Sal," she said, "but just don't expect me to bake for everyone. I have an idea those boys of yours can really eat. And drink coffee, too."

The day arrived, and right on the dot of 1 PM the boys started to arrive. Delmer was first, followed by Wayne, Dan, Louie the Flash, and Larry. They all brought sacks of baked goods and thermos of coffee. The last to arrive was Ron, who brought a large mixed flower bouquet for Sylvia, to recognize her generosity in opening her home to the Club.

It was a bit of a tight fit in Sal's basement, but he had gotten out a large folding table and folding chairs and there was just enough room for everyone. The boys drank coffee and munched on treats and talked checkers until finally Sal said, "Okay, let me put out a checker problem for you to solve. No one needs to buy treats today so solve it just for fun.

Sal went over to a large bookshelf which was overflowing with checker books, magazines, and newspaper clippings. He laid out the following position from a diagram in one of the magazines.

"This is a good one," he said. "Take your time and see how you do."

The boys dug in at once and the discussions became quite animated. Nearly an hour went by until Ron said, "We've got it, Sal!"

---

Sal's basement den looks like a nice place to be solving a checker problem. We hope you have a comfortable environment, too. Join the "boys" in solving this one, and click on Read More to check your solution.

[Read More]

Fundamentals. They are the basis of success in any sport. Knowing how to swing your bat or position to catch a fly ball in baseball. Blocking and tackling in American football. Making free throws in basketball. And there are fundamentals in our game of checkers, too.

Today we have something that's not quite a speed problem but does fall more into the novice or beginner category. It's a sound exercise in those checker fundamentals--- seeing a win when one is there and then carrying it out.

An experienced player won't have any difficulty with this one; if you fall into that category, see how quickly you can solve it. For the less experienced player, please don't give up until you find the solution, as it relies on relatively simple play that will score you many a point over the board. When you're ready, it's fundamental to know that clicking on Read More will show you the solution.

[Read More]

We're very pleased to be able to offer our readers the annotated match book from the 2024 U.S. vs. Italy international match, courtesy of Jim Loy and Alex Moiseyev (with support from John Acker and others). The book is available as a completely free download.

Anyone in touch with the international checkers and draughts community will recall that the first U.S.-Italy match, held in Rome in April 2018, was won by Italy by the smallest of margins. Nevertheless it was an important and significant win and a further demonstration of how the Italians had moved onto the checkers scene with success at the highest levels (two world champions, no less).

The much anticipated rematch, in Vidor Texas over the period July 1-5, 2024, ended in a victory for the U.S. with a recognizable yet not overwhelming score difference. Have things evened up and the tide turned back to the U.S.? It's hard to say; Italian players still hold both the 3-move and GAYP world championships.

More about this international tournament and the whole history of international tournaments can be found in the book. We're certain you'll enjoy the narratives and the games as expertly annotated by highly respected checkers writer and analyst Jim Loy. Here's one sample from the book.

To see the solution, just download the book and turn to page 6. The Checker Maven thanks Mr. Loy and Mr. Moiseyev for the opportunity to put this book before the checker playing public.

It all started with the five parts of Richard Pask's Logical Checkers, published as separate ebooks, and then later as a trade paperback edition combining all five parts into the single volume Complete Checkers: Insights. The first part was also published in trade paper format as Checkers for the Novice and has sold hundreds and hundreds of copies. Insights itself ran to a revised second edition, and now the next step has been taken.

The long-awaited hardcover version of Complete Checkers: Insights is at last available both as an ebook and a printed edition.

A year in the making, the book incorporates hundreds of changes, corrections, and additions. It's been completely re-typeset in a larger 8 1/4 by 11 inch two-column format, printed on cream paper and case bound. If we do say so ourselves, it's quite the book.

The electronic PDF version is available here, as always completely free of charge, making the book available to anyone, anywhere, regardless of location or financial means. The print edition can be obtained from the Amazon outlet serving your country or geographical region. It is priced very reasonably with the objective of just covering our costs and no more.

A hardcover of the companion work, Complete Checkers: Repertoire is in the works and should be available within another year.

Just to hold your interest, here's a sample position from Insights.

The solution is found on page 425. Don't wait; download the ebook and if you like it, consider supporting the project by ordering the printed hardcover if your means and inclination so allow.

The Detroit Doublejumpers of the National Checker League were on spring break, and their superstar captain, Marvin J. Mavin, had a week off.

Now recall that in our last story, Marvin got into trouble when his Valentine's Day gift to his wife, Priscilla, was a love poem written by a computer. It took Marvin a little while to make things up with her, but a $100,000 emerald ring was a good first step. However, there was to be a second step.

"You're forgiven," Priscilla said over Sunday morning breakfast in the breakfast room of her 5,000 square foot luxury condo, "or at least almost."

"Huh?" Marvin replied. "Ain't that fancy ring enough?"

"I do appreciate the gift, dear, even if it was a couple of weeks late, and even if the stone was a bit on the small side. However, there's one thing you'll need to do for me and then we'll say you've paid your debt to me."

"Do? Like what?"

"Well, seeing as how you're off this week, and seeing as how on Saturday night there's the annual black-tie fundraiser for the Art Museum, I thought you might help out."

"Black tie --- I ain't got no black tie."

"Oh, Marvin, we've been through this before. You'll rent from the usual place, Twirly Tuxedos and Gaudy Gowns. But that's not the point."

"So what is?" Marvin ws beginning to shake his foot and push his fork around his plate, sure signs of nervousness.

"Why, I've set up an exhibition! You'll play a game against your old friend, Dmitri Tovarischky. Attendees will bet on the winner, with all of the money going to the Art Museum. The one who bets the most on the actual winner will be named Patron of the Year, a great honor. Most attendees would pay several hundred thousand for that title."

"This is nuts!" Marvin exclaimed. "Dmitri ain't my old friend or any kind of friend neither. He's a total ---"

"Don't say it, Marvin. In any event complaining won't help. It's all arranged. You're committed."

"What kind a folks would pay a few hundred grand for some dumb museum title? And I ain't gonna play wearing no monkey suit. In fact I ain't gonna play at all!"

"I would be careful if I were you, dear. Yes, you are going to play. Yes, you are going to wear a tuxedo. And especially, you are going to be polite to the people who support the museum with large contributions. In fact, a little fawning, bowing and scraping might be in order."

The discussion didn't go on for much longer. Marvin knew there was no way out. But Dmitri? The very thought of him made Marvin ill. (Editor's note: Marvin's experiences over the years with Dmitri have been related in a number of previous Checker Maven stories.)

It was the night of the gala. Marvin had spent an uncomfortable couple of hours at Twirly Tuxedos getting fitted for a rental that would cost about $1,000 for this one event.

Marvin and Priscilla arrived at the downtown Swank Hotel at a fashionably late hour. The hotel ballroom was filling with men in formal attire, and women in evening gowns and sporting glittering jewelry. Admission alone was $50,000 per person. It was an affair for the wealthiest of the Detroit area's wealthy.

Dinner was something that was said to be duck but was surely the usual banquet rubber chicken, accompanied by unidentifiable side dishes. But, as it was prepared by a three star Michelin chef, everyone raved about it and said how it was well worth the $50,000 price of admission. Marvin started to make a remark about the food but Priscilla quickly cut him off. "Remember, Marvin, grovel a little tonight," she admonished.

There was a betting board for the upcoming checker match. The board only announced the total amount bet but didn't break it out by player or bidder. By the time the event's emcee announced that the match would commence in just 30 minutes, the total pool was at nearly ten million dollars. The emcee noted that betting was running quite a bit behind the previous year and that the patrons needed to hurry if they were to have a chance at becoming Patron of the Year.

Soon Marvin and Dmitri were called to the front of the ballroom, where a small stage had been set up with a table and chairs. An elegant checker set and board was on the table.

"Ladies and gentlemen," the emcee announced, "tonight two top professionals will contest a match for charity. The winner will be awarded the prestigious title of Art Museum Checker Champion and a generous grand prize of two museum entry tickets, good for use on any Monday morning of the winner's choice. That's a $20 value.

"The contestants will play on a diamond encrusted checker board, with ruby and ivory checker pieces. Use of this set was donated by Toys for the Rich Only, who stand ready to meet all your high-end requirements for one of a kind toys and games."

Marvin and Dmitri met at center stage amid great applause from the patrons. The betting pool closed at $15 million, which the emcee declared to have now exceeded the previous year's amount.

There was a very brief and unenthusiastic handshake between the two rivals.

"Checkers boy," Dmitri said, "we meet one time more and I am ready for crushing you again like last time."

"Uh, listen here you little Commie, I won that game as I recall, and I'm gonna win this one too."

"Checkers boy is dreaming," said Dmitri. "Prepare for humilating losing."

The match began. Other than the clinking of champagne and wine glasses, the ballroom was exceptionally quiet. All eyes were on the stage as the game progressed.

After about an hour, the following position was reached with Marvin to play.

Dmitri was grinning. "Now what," he said. "What you are going to do, checkers boy? I suggest resign. Save some time. I am wanting nice glass of champagne to celebrate victory and don't want to wait more longer."

"Stuff it," Marvin said.

The patrons knew the game was at a critical juncture. The silence in the ballroom broke and cheers of both "Marvin!" and "Dmitri!" went up. Finally, in the increasing din, Marvin made his move.

---

Did you ever play checkers wearing a tuxedo? We suppose it's possible, although surely not a common thing. Do you have a checker rival at the level of Dmitri's rivalry with Marvin? We certainly hope that if you do, you are on more cordial terms. But all that aside, would you be able to win this match? See if you can, and then click on Read More to see the solution and the rest of the story.

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In our previous Beacon Cafe story, Sal Westerman, the unofficial leader of the Coffee and Cake Checker Club, had been confronted by protesters who claimed that checkers was part of a Communist plot to ruin America.

Sal's club met on Saturday afternoons from just after Labor Day to just before Memorial Day with short holiday breaks. The year was 1955 and the venue was the Beacon Cafe in Bismarck, North Dakota, a locale that was about remote from Communism as anywhere.

The protesters had been dispersed by the police but their activities were far from over. One of them in an old Nash car trailed Sal on his way home. And then there were harassing phone calls to all the members of the club, but especially to Sal's home. His wife Sylvia had gotten quite upset, and Sal had gotten the police involved, but there wasn't a lot they could do.

However, it might all come to a head soon. One of the protesters' purposes was to have checkers eliminated from the public schools. Now Bismarck, like nearly all towns (in the alternate reality of our stories) had a thriving scholastic checkers program with teams competing at every grade level. But the protesters said that this was just a means of spreading Communism. They didn't present evidence except to say that there were red checker pieces, symbolizing Communism, and that players often played in teams, which apparently reflected anti-capitalist collective policy.

The school board would meet tonight to take up the matter, and Sal and the "boys" of the club (all but one of whom were over 50) would give testimony. Sal's testimony, as State Champion, would be expected to hold some weight, and it was also expected that saner heads would prevail. However, the outcome was still uncertain given the just-concluded McCarthy era.

That evening, a line of marching protesters greeted arrivals at the War Memorial Building, where the school board was to meet. Police were on hand to try to keep things orderly, but the protesters were on the rowdy and raucous side, chanting various slogans about the purported ills of checkers.

"There's their leader--- the chief Commie himself!" one of them shouted as Sal made his way to the entrance, followed by the rest of the "boys." Sensing potential trouble, a couple of policemen stood between the protesters and the checker club members.

Fortunately everyone made it into the building without incident. By the time 7 PM came around there were no seats left and attendees were standing in the back and on the sides of the main auditorium. At a few minutes after 7, School Board chair Janet Meyer called the meeting to order and ran through a number of routine business items with the rest of the Board.

At 8 PM, with some of the crowd growing restless, Mrs. Meyer turned to the final item on the agenda. "We have a proposal from a group called 'The Anti-Communist Anti-Checkers Coaltion'", she said into the microphone. "They have a petition signed by over 200 Burleigh County taxpayers, so we must take up their issue. I'll ask their representative, Mr. Gerry Russell, to present their case."

Mr. Russell took the podium to a mixture of cheers and boos, loud enough for Mrs. Meyer to pound her gavel and call for order.

"Checkers is a evil game," Mr. Russell began. "It corrupts our children by teaching them to love Communism and hate capitalism. It is anti-American and anti-church. Do you want your children to end up in jail for treason or seeking to overthrow our government? That's what will happen if we don't ban checkers from our schools, our community, and our nation! We are here to take the first step, casting this evil influence out of our precious school system."

Mr. Russell went on for a long while until finally Mrs. Meyer asked him to please conclude his speech.

"Very well," he said, "I'll end by saying I am a checkers expert and know everything about this horrid game. I was under its influence too for many years. But fortunately I was able to cast out the devil within me, and I saw the light. I pray that you see the light, too, and do what you know is right--- ban checkers in the schools!"

Mr. Russell sat down to more cheers and boos. Mrs. Meyer then said, "A local checker club, the Coffee and Cake Checker Club, led by Mr. Sal Westerman, the State Checker Champion, has asked to respond. Mr. Westerman, please come to the podium."

There were mostly all cheers for Sal as he made his way onto the stage although there was some heckling from the protesters.

"Thank you, everyone," Sal said in a calm and measured tone. "I am here to demonstrate the error of the ways of Mr. Russell and his group. Checkers, far from being evil, is a positive influence on a young mind. It teaches planning ahead. It teaches sportsmanship. It teaches our children to be gracious winners and resilient losers. It teaches the benefits of hard work and study. But it does more than that. It teaches how to focus and to think through a problem with persistence and attentiveness. It develops analytical skills which will serve for a lifetime."

"Prove it!" a protester shouted.

Sal smiled. "That is my intent," he said. "Mrs. Meyer, may I use the projector?" When permission was granted, Sal put a transparency with the following diagram on the projector's plate and projected it onto the screen at the front of the auditorium.

"Now, Mr. Russell, as you say you know everything about checkers, I challenge you to come up to the stage and solve this checker problem. Surely you should be able to do that."

Mr. Russell, sitting in the front row, was clearly taken aback. "A checker problem? How dare you expose the attendees to such evil! I will not come up and participate in this shameful activity! You may be a Communist, but I am not!"

"Come now, Mr. Russell, the checkers on the diagram are black and white. There's not a trace of red." That elicited a laugh from the audience but a scowl from Mr. Russell.

"Very well then, you just move ... wait a moment ... no, you move ... hmm ... it must be ... "

"Five minutes, Mr. Russell," Sal said. "That's enough time for any expert to solve it."

Mr. Russell had turned pale and had begun to sweat. "Fine, you play ... no, that's not it ... okay ... "

"The clock is ticking, Mr. Russell," Mrs. Meyer said, "and I think we are all interested in how this will turn out."

---

Sal has put his opponent on the spot. Will Mr. Russell be up to the challenge? Are you? While for Sal the stakes are high, you can solve the problem at your leisure and just for your own pleasure. When you're ready, click on Read More to see the solution and the conclusion of our story.

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It looks like someone is over on the side of the road. That might be okay, or it might not. It depends on the circumstances.

In today's speed problem, all of the pieces are on the side of the road, but White especially is sidelined and a piece down besides.

There's a draw here, and it won't be a lot of trouble for you to find it. See how quickly you can solve this one. An expert should see it at once but the problem is well within the range of an attentive novice. Don't stand on the sidelines; solve this one and click on Read More to verify your solution.

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In today's Checker School column, we continue with what Andrew J. Banks, in his eclectic book Checker Board Strategy, calls a "beginner's problem" although he does make something of a retraction of that statement, as we shall see.

Mr. Banks tells us that a problem whose terms contains the phrase "Either to Play" is known as a twin, for fairly obvious reasons. He gives the following example.

Although we've shown this from the White side, the terms in fact do hold. We don't see a lot of problems of this type and it's quite interesting. Is it, in fact, easy enough for beginners? Mr. Banks recants by saying, "Tough problem for a BEGINNER!!!"

Tough or not will depend on your skill level but we think it will entertain most everyone. Find both solutions, if you can, and then click on Read More to see the solutions.

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