The P=NP problem in computer science is one of the Millennium Prize Problems and if you can solve it, you'll win a cool $1 million prize from the Clay Mathematics Institute. We won't attempt to explain the problem here but it certainly can be said to be at the ultra-difficult level. The prize is yet to be claimed.

Turning to checkers, we recently we presented Brian Hinkle's Prize Problem which carried with it an award of $100 (not $1 million) to the first correct solver. Alas, that reward went unclaimed. Today we have a different sort of prize problem. It was published back in 1907 in the Canadian Checker Player magazine. The prize was a six-month subscription to that excellent publication of bygone days, and the prize was indeed awarded to a successful correspondent.

We'll not claim that the problem is up to Brian's grandmaster composing standards, nor will we offer anything beyond personal satisfaction for finding the solution. But it's nevertheless an interesting composition.

Would you have won a half-year subscription to one of history's best checker publications? We'd offer you a free six month on-line subscription to The Checker Maven but that wouldn't be much of a prize given that our publication is already free. So solve it just for the fun of it, and claim a look at the solution by clicking on Read More. If you like, write to us and tell us if you might have been a winner well over a century ago.

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Uh-oh. Someone is going to have to get out that spare tire, and no matter how many times you've changed a tire on the road, it's never much fun.

There are other kinds of spares, of course. There is spare time (a rather rare commodity in the Checker Maven offices). You can be "spared" something unpleasant, like a visit to the dentist. A spacious home has "room to spare" --- and so on.

In today's Checker School column, we present a very old position attributed to William Payne. "Spare" also has a meaning in checkers, as you'll see.

Of course, the problem is extremely easy and will be solved in a couple of seconds by players with even a moderate level of experience. But after you solve it, use a spare couple of minutes to click on Read More to see what point Andrew J. Banks, author of Checker Board Strategy, was trying to make.

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It was the big day. This Saturday, the North Dakota Open would take place with the winner declared the North Dakota State Checker Champion. This year, 1955, the tournament was taking place in the famed Silver Ballroom of the Patterson Hotel in Bismarck.

Sal Westerman and the "boys," all of whom were at least 50 years old, wouldn't be meeting at the Beacon Cafe this afternoon, as several of them, including Sal, were competing in the tournament.

The format was simple. The tournament would use the "Swiss" system with three rounds in the morning and two in the afternoon. Players with equal tournament scores would be matched against one another. Play was divided into the Championship Division and the Minor Division.

Gerhardt G. Grossvater of Minot was the defending champion and the favorite to win. Other top seeds were Professor Don Steam from Fargo, Danny Dan Daniels from Dickinson, and Bismarck's own Sal Westerman. But there were numerous other strong players and upsets were known to happen.

There was an air of excitement in the ballroom as the early rounds were played. One by one, the lesser players were defeated by the greater. Professor Steam, however, was upset by a player from Beulah, Pawel Patschpawkoski, who was now in the top four along with Danny Dan, Sal, and Gerhardt.

At the lunch break, Sal and a couple of the boys, Delmer and Wayne, went downstairs to the Rainbow Bar for a quick burger.

"What do you think your chances are, Sal?" asked Delmer.

"I don't know. I play Danny Dan and I think I have good chances. My record against him is almost all wins. And I don't think this Pawel fellow, good as he must be, can take out Gerhardt. That would leave me to play Gerhardt in the final round, which has never worked out for me."

"Come on, Sal," said Wayne. "You'll do it this time for sure."

But Sal didn't look so confident. The boys finished their lunches and went back upstairs a few minutes before the final rounds were to begin.

Sal was right. He won against Danny Dan, but the game was a close one. Gerhardt easily disposed of Pawel.

It was four o'clock and time for the final round. Gerhardt and Sal, the only players with a perfect score of four points so far, would once again play for the title.

Gerhardt was certainly polite enough, though he had just a bit of a swagger about him. Perhaps, as many-time State Champion, he felt he had earned it. For his part, Sal looked a little worried. Gerhardt was more than just good. He held his own in national tournaments, let alone in North Dakota.

The game began. Spectators thronged around the playing area. This was the game of the year, the one that would crown the Champion.

Sal gained a little confidence as play went on. Gerhardt, on the other hand, seemed frustrated at not being able to force a quick advantage.

The game took some odd twists and turns. Numerous kings were crowned but still the game stayed close. Finally Sal went a piece up, having four kings and a man to Gerhardt's three kings and a man. Could this be Sal's moment?

But the win, if any, looked tough. Gerhardt, having made a move, looked over at Sal, extended a hand, and said, "Draw?"

Sal was surprised by this. Gerhardt played games to the very end, almost never resigning and seldom even offering a draw unless the position had no play whatsoever left in it. Did this mean, Sal wondered, that Gerhardt might actually be in a loss and was bluffing?

"Thank you, but let's play it out," Sal replied.

"You won't take a draw against the great Gerhardt G. Grossvater, someone against whom who have a lifetime score of zero?" Gerhardt replied.

Now the crowd murmured. Gerhardt was known to have something of an ego, but this was a bit much.

"Quiet on the floor!" Referee Julian Jaegerlitz called out. Sal, for his part, did not reply. He thought for a minute or two, and then simply said, "Here," as he made his move.

---

Can you win this one? For Sal, his first ever State Championship hangs in the balance, but for our readers, there's no pressure, just the enjoyment of solving a fine problem (it's by Brian Hinkle). See you how do and then click on Read More to see the solution.

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No, the folks above aren't talking about a movie or a video game. They're actually touting a summer camp, packed with active rather than passive adventure. Sounds good to us.

This month's speed problem is action-packed, too--- and quite active. Solve it and see why.

We'd say it's on the upper end of easy in difficulty, not quite medium, but certainly not trivial and very nice. Skilled players won't need a lot of time. The rest of us might need a little longer, but it's definitely within reach. Take action, try it out, and then click on Read More to check your solution.

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The new season of the National Checker League was ready to start, and in a very special way. The reigning World Champion team, the Detroit Doublejumpers, had traveled to Chigasaki, Japan, along with the San Franciso Souters. They would play the season opener in front of over 50,000 Japanese checker fans in the Chigasaki Checkerdrome.

Checkers in Japan was really big, nearly as big as the national game of Go. Japanese checkerists dreamed of earning a place on a National Checker League team, and in fact the Captain of the Souters, Tadeo Tachikawa, was a native of Chigasaki! He was a local and national hero and the Checkerdrome had sold out within minutes after sales began, even at the startling equivalent price of $250 per ticket.

The teams had been given a series of protocol lectures by US State Department officials prior to their arrival. They were to carefully observe all Japanese customs and represent both the United States and the National Checker League in a dignified and honorable manner.

That all went quite well for the two days of ceremonies prior to the big match. At least until the banquet on the evening prior to the competition.

Now, Marvin J. Mavin, the superstar Captain of the Doublejumpers, had the best of intentions. He listened carefully during the protocol lectures, and then asked questions of his girlfriend, Priscilla, a high-ranking executive who had made many business trips to Japan. Marvin learned to say a few words in Japanese, like "konichiwa" and "arigato"; he bowed when appropriate, and made every effort to be polite.

It was just that the Japanese beers were so good. Fresh and flavorful, and served icy cold, they just hit the spot, especially after the very strict summer training camp regimen Marvin had gone through.

Of course, his Japanese hosts, who had mastered the art of hospitality untold centuries ago, saw how much Marvin enjoyed their beer, and kept bringing him refills throughout the course of the banquet. And it was a rather long banquet, replete with speeches, toasts, and ceremony.

So when it came time to leave the 5-star hotel where the teams were hosted and go to the Checkerdrome early the next afternoon, Marvin was notably absent at the bus loading area in the back of the hotel.

"Go find him!" roared Coach Ronaldson. "I want him inside the bus in no more than five minutes!"

Assistant Coach Joe Radler and Trainer Bobby Berkowitz ran off into the hotel and hurriedly summoned an elevator to the 30th floor. They both knew what they would find, just as did Coach Ronaldson, even though he had said nothing.

Pounding on the door of Marvin's room yielded no results. Luckily, Trainer Berkowitz spoke Japanese and was finally able to get a hotel worker to open the door, citing an emergency situation. But that took well over an hour. The worker had to consult with his manager, who had to call hotel security, who passed the decision up to the hotel manager. Meanwhile Assistant Coach Radler received a text from Coach Ronaldson saying that they couldn't wait, the bus had left, and to take a taxi to the Checkerdrome as quickly as possible.

Marvin was in the bathtub of his suite's sumptuous bathroom, soaking in soapy water, oblivious to everything.

"Marvin! Marvin!" shouted the Trainer. "We have to go to the Checkerdrome! Now!"

"Hey, hey," Marvin said, his voice a bit slurred. "Too loud, bro! My head ain't feelin' so good ... and ... hey ... what time is it anyhow?"

"Four in the afternoon," the Trainer replied. "The bus left at two thirty. We play at five sharp and it's an hour by taxi to the Checkerdrome."

"Bus? What bus?" Marvin said. "Uh ... oh ... yeah, we play today ... I kinda spaced that out ..."

"OUT OF THE TUB! NOW!" the Assistant Coach shouted. "I don't care if you have the biggest headache in world history!"

It took Marvin another twenty minutes to dry off, get into his uniform, and get down to the lobby.

The taxi went as fast as it could, but the driver would not speed or otherwise break the law. Trainer Berkowitz heard him mutter something about disobedient Americans having no respect, but the Trainer didn't reply. The driver, after all, was right.

When Marvin finally came out on the field, it was five thirty. The match had long since begun and Marvin's clock was running down. "The only reason I didn't sub for you," Coach Ronaldson hissed, "is that a lot of people paid a lot of money to see you play. But you're in big trouble. You're not getting away with this."

Being late was a tremendous breach of protocol and a huge gesture of disrespect toward Marvin's opponent, Tadeo Tachikawa. Marvin was greeted with stony silence when he took the field. The Japanese crowd did not appreciate having their customs dishonored. Though too polite to boo, failing to cheer and applaud communicated a clear enough message.

Tadeo stood and bowed. Marvin awkwardly returned the bow, and stammered an apology. "Let us play," Tadeo simply said in return.

The game commenced. Marvin was hardly at his best and Tadeo was a very strong player, aided by having much more time on his clock than Marvin did. The game finally reached this point.

Marvin knew he was in a difficult position. His clock was down to six minutes. Could he at least find a draw? He tried to focus but his head was pounding. If only ...

With just two minutes left on his clock, Marvin played 22-26.

"Oh, Marvin-san," said Tadeo, "I am so sorry."

Marvin looked puzzled. "Huh? Say what? I ... oh."

---

Did Marvin miss a draw? Our hapless hero seems to be having a difficult day, albeit one of his own making. See if you can correct Marvin's move and then find Tadeo's win. When you're ready to see the solution and read the rest of the story, click your mouse politely on Read More.

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"Kingless" in chess isn't possible. The White King must be somewhere. The above chess position was originally presented as a "find the White King's square" puzzle. Unfortunately the puzzle is trivial and flawed with multiple solutions.

"Kingless" in checkers, on the other hand, is quite a normal situation.Contest 58 in Bill Salot's spectacular long-running Unofficial World Championship Checker Problem Composing Contest series has begun. and the theme of this contest is indeed Kingless. It features four disparate problems, all of whose settings contain no kings. However, this set of problems is free of multiple solutions and certainly isn't trivial.

The contest can be found, as always, at contests.checkermaven.com. It runs until the end of October. Be sure to try out the problems and cast your vote for the one you think should win the title.

For today's problem, Bill provided us with a "sample" kingless problem. It's not part of the contest but it illustrates what you have to look forward to. The problem is entitled Bewildered and is by well-known composer Roy Little.

Bewildering? Perhaps. You don't need to be the king of checkers to solve it, though; it's within reach if you put in the effort. When you're ready, give your mouse a kingly click on Read More to see the solution.

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Editor's Note: At the Beacon Cafe, it's always 1955. We rejoin our intrepid checkerists now in September of that year. It's the Saturday after Labor Day, and with the summer season at an end, the "boys" (all of them over 50 years of age) return to their Saturday afternoon sessions in the large booth at the back of the cafe, enjoying a few hours of problem solving, skittles games, baked goods, coffee, and good companionship.

---

Everyone in North Dakota enjoyed summer, brief as it was, and Sal Westerman, the informal leader of the Coffee and Cake Checker Club, was no exception. Still, no one could be happier when September rolled around and his club started meeting once again.

Apparently the other members felt the same way, for today there was a big turnout, with Dan, Wayne, Louie, Mike, Delmer, and even Spooler, Tom, and Ron, the latter three of which weren't seen quite as often.

Deana, the proprietress and the best baker anyone had ever met, was smiling broadly. She enjoyed having the "boys" come in on what would otherwise be a slow Saturday afternoon. "Zucchini and oatmeal chocolate chip cookies today," she announced. "Fresh and hot."

There were sounds of approval from the big booth where the "boys" were. "Sal's buying today!" Spooler piped up.

"Okay, Spooler, I'll buy," Sal said, "but only because I'm so pleased with today's turnout." Addressing Deana, he said, "A couple of large plates of cookies and coffee all around, on me!"

"You got it," Deana replied. She had already started stacking plates with her warm, fragrant cookies.

"State championships are in Bismarck this year," Sal added. "Next week, even!"

"Yup, over at the Patterson Hotel," Wayne said. "Usually Fargo or Grand Forks gets the bid, but not this time."

"Is everyone playing?" Louie asked.

There were nods all around. Traveling to Fargo or Grand Forks wasn't always feasible, but having the tournament right there in Bismarck made it just about a must-do event.

"Think you can win it, Sal?" continued Louie.

"I don't know," Sal said. "I pretty much took care of that Steam fellow last spring, but Grossvater up in Minot will likely take it." Gerhardt G. Grossvater was the reigning State Champion, a title he'd held for ten years straight. (Professor Steam was from Fargo--- see previous Checker Maven stories.)

"You might have a shot at it," Ron said. "You haven't played in the tournament for a couple of years and maybe you'll win this time."

"I last played Grossvater in '52 when the tournament was in Minot. He won in the finals. I've never been able to beat him," Sal said.

"Well, tell you what," Wayne said. "I found a problem that your friend Ed from Pennsylvania published in All Checkers Digest quite a while ago and I brought it along. How about you all try it out? It's called 'Head Bumper.' That'll give everyone a little warm-up for next week."

"Lay it out," Sal said. Sal was the one that usually brought along a challenging problem or two, but today he was happy to be on the solving end.

"Okay, here you go," Wayne replied, and set out the following position on a couple of the checkerboards on the booth's table. "See if you can get it in an hour or so while we sample these cookies." Deana had just set two plates of cookies on the table and was refilling everyone's coffee mugs.

"Hey, this is a good one," Sal said. "We're going to need that hour."

Cookies in hand, the boys got to work.

---

A warm-up problem is good for everyone, even if you're not planning to take on a tough opponent like Gerhardt G. Grossvater. With or without zucchini oatmeal chocolate chip cookies, see how you do, and then click Read More to check your answer and read the rest of our story.

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It's Labor Day weekend at the time of publication of this column, and on Monday, we recognize and celebrate the contribution of workers in all walks of life. The drawing above shows just a few of the many ways in which people contribute. There are lots more, and we've always said that we think all honest work is praiseworthy and honorable.

After some really tough times, we're happy to note that America is getting back to work, and in fact the demand for workers is high. So let's give Labor Day an extra measure of emphasis this year and enjoy the day as never before.

We usually turn to Tommie Wiswell for a problem on holidays such as this, but instead today we've got one that Tommie selected for inclusion in one of his books. It's by William Link, who composed this problem while still playing as a youth in New York City a nearly 80 years ago. Mr. Wiswell viewed him as an up and coming champion, but we've not heard or read much about him. Perhaps something derailed his checker career? We don't know, but we do know that the following position, which Mr. Link called Out on a Limb is an interesting one. Mr. Wiswell calls it "simple, pleasing, and instructive."

You should be able to solve it, but if you can't, you won't be out on a limb, as clicking on Read More will show you the solution.

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Our Prize Problem contest, sponsored by Brian Hinkle, has ended. No, we can't offer the Nobel Prize, but Brian did offer $25 to the first person to solve it. He later upped his offer to $50, then $75, and finally $100.

But no one submitted a correct solution so Brian got to keep his money.

For those of you truly puzzled by the problem (which must be just about everyone), don't feel bad. The two most powerful computer engines in the world, KingsRow and Cake, couldn't solve it either! Here's Brian's solution and brief notes.

3-7 10-15 7-10 20-24 21-17---A 24-27---B 11-7 2x11 10-6 1x10 22-18 15x31 17-14 10x17 25-22 17x26 5-1. White Wins.

A---Planning ahead for the fireworks.

B---16-20 25-21 24-27 11-7 2x11 30-25 23x30 32x7. White Wins.

White is down no less than six pieces, but still wins as Black will eventually run out of moves in this incredible block position. Marching the checkers on 11 and 4 down the main diagonal won't work as White will simply allow his piece on 29 to capture both of Black's approaching men. Try working through it on your own. You won't find a single variation in which Black doesn't eventually become completely blocked.

Block problems, along with fortress problems and "fugitive king" problems are notoriously difficult for computers to solve, and Grandmaster problemist Brian Hinkle has here created what may be the ultimate block problem of all time. We hope you enjoyed it as much as we did. In fact, if you'd like to see another Brian Hinkle classic, check out Bear Claw, published back in the early days of The Checker Maven.

Summer training camp wasn't Marvin J. Mavin's favorite thing. Not at all.

Every August, before the start of the National Checker League regular season, the championship team which Marvin captained, the Detroit Doublejumpers, held training camp at a classy resort near the appropriately named town of Au Train in Northern Michigan. Training camp was no joke to Head Coach Ronaldson. He put the ten players on the Doublejumper team through a rigorous program of study, competition, and even intense physical training, as the players had to be able to withstand the long hours that checker matches could occupy.

Marvin, after previous bad experiences, knew better than to arrive out of shape, lest he be made to run laps up and down the lake for what seemed like forever. He also knew better than to bring along a bad attitude ... or a craving for a cold beer. The Coach was very strict about things like that, even limiting the amount of coffee his players were allowed.

This year Marvin thought he was as ready as he could possibly be. He had spent a lot of time with his girlfriend Priscilla, and they had frequently jogged and worked out with weights in Priscilla's extensive home gym. He allowed himself just one beer after a workout and none at all during the rest of the day. And whenever he made a smart remark, Priscilla instantly scolded him.

It didn't work out the way Marvin had hoped and expected.

A couple of days after reporting for camp, Coach Ronaldson, at the daily morning team meeting, introduced a new person.

"I'd like you all to meet Betsy Batsy. I've recruited her and she's agreed to try out for the team."

"I'm going to be the Captain," Betsy interrupted in a deep voice. "I'm going straight to the top and you over there ..." pointing at Marvin " ... aren't going to stop me. I'm going roll right over you and ..."

"Thank you, Betsy, I'm sure we all appreciate your ambition," Coach Ronaldson said. "I met Betsy at a Checker Barrel restaurant. She was giving an impromptu exhibition at those tables they have outside and I watched her beat 50 players at once. There was even a AAA pro in the group. Now, although Betsy has never played professionally ..."

"I can beat any pro there is," Betsy blared. "You, him ..." (again pointing to Marvin) "... anyone."

"Well, I did play a few games with Betsy after her exhibition, and uh ..."

"I kicked you in the pants," Betsy said, guffawing.

"Well, yes, Betsy won every game, actually. So I thought someone this good, who by the rules could be recruited outside of the amateur draft, might be a real addition to our team."

"I can replace your whole team," Betsy stated. "Just me. I can play every board in every match and win the championship all by myself."

Although no one spoke up, the Doublejumper team, and Marvin in particular, were really wondering. Was this Betsy that good that the Coach, who was always strict, would put up with her attitude? It all seemed really strange.

"Come on boys," Betsy said, addressing the team, "or should I say girls?" That got a stern look from the three women on the Doublejumper team. Betsy noticed and said, "Sorry, girls, I should have said 'babies.'"

"Okay, team, set 'em up," the Coach said, "ten boards. First team and second team. Betsy is going to play a simul against all of you. Then you'll see she deserves a place on the team. Of course, that means one of you will get sent down to our AAA farm club, but that's how it goes."

"Him," Betsy said, pointing to Marvin. "He's the one you're going to send down.

"Uh, well, that's up to me ..." the Coach said.

"You want me to play for you, you do things my way," Betsy stated flatly.

But the boards were set out and play began. The Coach decided on single elimination. In the first round, Betsy defeated eight of the ten players, all of whom were eliminated. She drew with second board player Pete Butterworth and lost to Marvin on first board.

In the next round, second board was again a draw, meaning Pete was eliminated. But Marvin won again.

"Just you and me," Betsy said to Marvin, "mano a mano. Ha ha! You just won those games because I was playing more than one opponent. Now I crush you like the bug that you are. And the rest of you ... " Here Betsy looked around at the other team members. "The rest of you are off the team!"

"Wait a minute, now," Coach Ronaldson said. He was starting to wonder if he had made a big mistake. But he said no more, as the playoff between Marvin and Betsy had started.

The game reached the following position with Marvin to move.

"You're finished, little buggy boy," Betsy teased. "Squashed! Like a filthy roach!"

"That's it," said Coach Ronaldson. "Miss Batsy, I invited you here to try out for a place on the team. You're a great player but I won't put up with any more of your bad attitude. If you want to play professional checkers, you can go try out for one of the Rookie Leagues and see if they'll want to deal with you."

"Coach, let me finish this game, okay," Marvin said. "Then old Batsy here can go hitch a ride back to ... wherever she came from."

"As you wish," the Coach replied. "Finish your game."

Marvin made his move.

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Betsy Batsy is a tough opponent, but Marvin seems pretty confident. Can you find a win here, or will Batsy Betsy bat you down to the minor leagues? See how you do and then click on Read More to see the solution and the conclusion of our story.

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