Contests in Progress:
There are transpositions in music; music in one key is transposed into another. It's something that's familiar to all music students.
There are also transpositions in mathematics; the one shown above is from the branch of study known as group theory. We won't try to explain it here as it's more than a bit out of scope for a checker column.
What is in scope of course, is a transposition in a checker game. Transpositions are common in the openings, when one opening line, whether through a different order of moves or other means, transposes, or changes, into another opening line. (The concept can of course be generalized beyond openings.)
Jim Loy has put together a comprehensive booklet of opening transitions, and has generously offered it for free publication on our Checker Maven website. You can download the book here.
As an example, and today's problem, here's a landing known as the Pioneer, which can be reached by transposition from six different ballots.
White now plays 29-25. If Black follows with 4-8, he falls into a losing position known as Dunne's Loss, as shown below.
What should Black have played instead?
Your task is to correct the losing move (not so hard) and to work out the White win, rather an advanced challenge, but instructive nonetheless. So see how well you can do, then click on Read More to see the winning play.[Read More]
Tommy Wagner had made Varsity on his high school team in central Florida. Except it wasn't quite as simple as all that.
In our last story, Tommy, as a freshman, was ready for spring tryouts. He had an outstanding record as Captain of the Junior Varsity team, and he did well in the tryouts and also during training month in August. Coach Schann had named him to the Varsity team in view of his progress.
But that was the Varsity second team. The first team consisted of a titled Master and four Experts, and Tommy, though now at the very top of Class A, fell somewhat short. Tommy ended up on third board on the second team, and it meant he wasn't a starter and would only fill in as a substitute for first team.
Of course, he played in the second team matches, and got to play a couple of times as a first team sub during the fall, but as Christmas vacation rolled around, he was feeling a bit down. Second team matches didn't get anything like the attention that the first team got. No playing in front of big cheering crowds. No being something of a local hero in the high school halls.
It was Saturday morning, and Tommy had arrived a few minutes ago at Uncle Ben's place. Now, Ben wasn't really Tommy's uncle but everyone called him Uncle Ben. In fact he was a former professional checker player, who had some years ago wrapped up a great career and retired to Florida. He now did a little tutoring of promising young players.
Tommy went for a lesson at Uncle Ben's nearly every Saturday. They would sit out on Uncle Ben's front porch, usually with a pitcher of Uncle Ben's wonderful homemade lemonade, and study checkers for a couple of hours. Uncle Ben was a great coach, and often taught Tommy lessons that went beyond checkers and into coaching for living.
Today Uncle Ben could see that Tommy was despondent, and rather than starting out with a checker problem for Tommy to solve, Uncle Ben poured out the lemonade and decided to just chat for a little while.
"So what is it, Tommy? What's on your mind? You've made Varsity, that's a big accomplishment for a young player. Not everyone makes it at the start of sophomore year."
"I know, Uncle Ben," Tommy replied, "but it's third board on second team, and I only got to play twice in league competition, as a last minute substitute on fifth board when coach decided to give me a little experience. I want to be on the first team and play all the matches."
"Well, Tommy, it seems like we've had similar discussions before, about earning things and being patient."
"I know, Uncle Ben, the first team players are all better than I am. I get it, I really do, but I just want to play. When I was on Junior Varsity, at least I got in a lot of time on the board."
"So, what do you think it will take for you to move up to first team? What do suppose Coach Schann is looking for?"
"For me to improve? I mean, that has to be it, I have to get better, I guess, good enough to compete with those Experts and Masters on first team."
"Exactly, Tommy. Your coach will move you up when you're ready, no sooner and no later. Things don't come to us just because we wish for them. They come because we work for them. Do you know, when I first made it to the Major Leagues, when the Houston Huffers called me up, I sat on the bench for quite some while? I'd get to play every so often but the top players got the glory. I was a sub, just like you are. It wasn't easy, but I kept practicing and working, even though I had already made the Big Show. Then, one day, I got my chance, and I never looked back."
"Gee Uncle Ben, you think I can do that too?"
"Of course you can, Tommy. You worked your way up to Captain of Junior Varsity and then you earned yourself a spot on Varsity, even if it isn't as a first team starter. So you've got what it takes, and I suspect that by the latter part of the season you'll be playing more often. But only if you keep up your studies--- and maintain a positive, can-do attitude."
"Well, I'm ready to do what it takes, Uncle Ben."
"Very good. So let's work extra hard today. Here's a problem for you to study, and we'll do several more when you get this one. It might turn out to be a long morning, but we've got lots of lemonade."
Uncle Ben set up the following position and Tommy, who at times needed a reminder that patient hard work precedes success, dug right in.
If we don't miss our guess, you, our reader, aren't a second team Varsity player at a local high school, although one never knows. But you're here because you're a checker fan, and you've likely long ago learned that mastery of checkers doesn't come overnight. Can you solve Uncle Ben's problem? See if you can, and then click on Read More to see the solution, notes, and numerous additional examples of the theme.[Read More]
April 15, the normal due date for income tax returns in the United States, falls on the day of publication of this column. However, being a Saturday, returns won't be due until the next business day, or Tuesday, April 18 (Monday, April 17, 2023 is a holiday in Washington, D.C.).
Marvin J. Mavin, the superstar captain of the champion Detroit Doublejumpers in the National Checker League, had yet to file his taxes, and his fiancee, Priscilla Snelson, wasn't pleased or amused.
Priscilla was the CEO of Rust Belt Holdings, a Detroit based multinational conglomerate, and a team of Certified Public Accountants completed her income tax filings every year. She had a compensation package which ran to about $5 million a year base pay, which doubled with bonuses and stock options, and strived to pay the minimum amount of tax, hence the highly qualified team of experts in her hire.
Marvin was visiting at Priscilla's condo that Saturday afternoon, and of course he was fully occupied solving checker problems in the latest issue of All Checkers Digest. Or at least trying to solve them, as Priscilla was definitely on Marvin's case about his not filing his income taxes as yet.
"Marvin, you make fully half as much money as I do, with your $5 million a year 10 year contract with the Doublejumpers. Why don't you have your own team of accountants? Or just hire mine, they'd be glad to help."
"Yeah, for about $50,000 they would. I don't need those guys."
"They're not all guys. They're about half women, and very talented, and you do need them. In fact I've already ... "
"Aw, Prissy, geez. I just use good old LightningTax, you know, on line, and for like a hundred and fifty bucks everything gets done in half an hour and then I can get back to my magazine. See, look, here's one by that guy Ed in Pennsylvania that I'm working on."
Priscilla walked over to the Italian leather couch where Marvin was sitting, pulled his magazine out of his hands, and threw in onto the quartz crystal coffee table. "You pay probably twenty times the tax you ought to pay. And don't call me Prissy!"
"Aw, honey, like, I ain't got nothing to deduct. My paychecks go into that there Blackguard account and they put some in my checking, and it's sorta real easy. I don't need to worry about nothing."
"Sure. You own a beat up old Volkswagen, you rent a grungy apartment in a terrible neighborhood, you don't have any investments other than that one Blackguard index fund, which by the way I set up for you, and ... you earn a great deal but you just don't care about your money!"
"Yeah, 'cept, I, like, you know, got enough and stuff and I don't need nothing."
"Well, let me tell you, fiance of mine, when we get married your attitude will be a big liability because then we'll have to deal with joint filing, and things are going to change. Big time. I won't let you waste our money like you're doing now. Do I make myself clear?"
"Ah, yeah sure, whatever you say." Marvin reached for his magazine but Priscilla pulled it off the table and tossed it across the room.
"Now, Marvin, you will be doing your taxes right now. As I was starting to say earlier, I've made arrangements for you. Sylvia Yang is coming here and she'll arrive momentarily. She's a senior partner at FatFingers, the accounting firm I use. You'll treat her with respect and deference and you'll do exactly what she tells you to do, immediately and with no argument or discussion."
"Right now? But you didn't tell me nothing about that and I was busy with my magazine. There's that real good problem ... "
"You'll have a really bad problem if you don't listen."
Marvin, through long experience, knew when arguing would just make things worse, and at that moment, the intercom sounded. It was the doorman of Priscilla's condo building.
"Ms. Snelson, there is a Ms. Yang to see you."
Priscilla pressed a button on the intercom. "Thank you, Jackson, please send her up."
A few minutes later there was a knock on the door. Priscilla pulled the door open an in swept a woman dressed smartly in business attire, carrying a leather briefcase with gold hasps. She went immediately to the conference room (Priscilla had a very upscale condo), sat at the table, took a laptop from the briefcase and started it up.
"Mr. Mavin?" she called. "Over here, please, we must start at once."
Marvin slowly got up from the couch, took a longing glance at the checker magazine lying in disorder in the corner of the living room, and entered Priscilla's conference room.
"I'm Senior Partner Yang," the woman said. "Don't bother attempting to shake hands, there is no time to waste on pleasantries."
"Uh, okay, yeah ... "
"Sit down, Mr. Mavin. The first thing I need from you is a retainer check, and you'll need to sign our retainer agreement. I think $25,000 will be sufficient to start, and we'll bill you for the balance later on. So if you would kindly get out your checkbook ... "
"Uh, I ain't got it with me."
Ms. Yang gave Marvin a deprecating glance. "Oh, really? You're that unprepared? All right then, we'll take a credit card for a three percent upcharge. You do have a credit card, don't you?"
Marvin shrugged his shoulders and got out his 10 year old duct-tape wallet. He had a feeling that the next few hours wouldn't be very pleasant.
It seems to happen often. Poor Marvin doesn't get to solve an interesting checker problem, and instead needs to follow Priscilla's directions. Or else.
Now, you may not have a $5 million per year 10 year contract with a professional checker team (or do you?), but you can work on today's problem at your leisure. That's something, at least!
When you're ready, you can click on Read More to see the solution. We promise not to bore you with the details of Marvin's afternoon as Senior Partner Yang from FatFingers completes his income tax returns. Suffice it to say that a fun day was not had by all. Or at least not by Marvin.[Read More]
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Cutting your lawn very short, perhaps too short for the good of the lawn, is often referred to by a term which is now considered politically incorrect and offensive to some. The word in question supposedly shouldn't be used any longer.
But an alert reader pointed out that, in our republication of Willie Ryan's Tricks Traps & Shots of the Checkerboard, we omitted an entry called Scott's Sc*lp*r. We're remedying that omission with today's column and have renamed it Scott's Close Shave, which we hope will make the LTBO ("Looking To Be Offended") crowd happy.
Let's let Willie give an introduction in his own words.
"The feature performers in this draughts drama were Robert Jackson and A. B. Scott, two of England's foremost players at the turn of the century. Sir Scott, who handled the white pieces, was a sagacious specialist in the management of weak, off-color, or radical moves, which in most cases he had carefully analyzed and prepared in advance. It is evident from Champion Scott's fine play in the game below, that he was thoroughly familiar with all aspects of the formation into which he lured his opponent, enabling him to spring the hair-raising finale at the diagrammed stage."
Willie's analysis of this game is uncharacteristically flawed. The KingsRow computer engine uncovered some very interesting play. Here's the complete run-up, with notes.
Lettered notes are by Willie Ryan. Numbered notes are by your editor.
A---A powerful attacking move developed by Robertson, Martins, and Wyllie.
B---With this move, Jackson passed up his last chance to draw, but who would ever believe that his choice was to be invalidated in the manner shown? The correct continuation at B is: 6-10, 17-14, 10-17, 21-14, 13-17---5, 22-6, 15-31, 24-8, 31-24, 28-12, 2-27, yielding a draw. John Robertson.
1---Willie didn't note this, but the move appears to lose according to KingsRow.
2---2-7 would have kept a stronger advantage but Black may still have a win.
3---Turns a probable win into a possible loss. Willie's analysis isn't quite correct. See note B above.
4---A mistake that loses at once. 6-9 would have given Black better chances although he's still in a possible loss.
5---This move is hard to understand and throws away the win. 3-7 is correct here. Perhaps the spectacular exchanges diverted Willie's attention.
Do you see the White win from the diagrammed position? Work it out and then click on Read More to check your the solution.[Read More]
This had never happened before, not in all the years that Sal Westerman had been running the Coffee and Cake Checker Club.
Regular readers will be familiar with our setting; a version of Bismarck, North Dakota, where it's eternally 1955, and in the Provident Life Building near downtown Bismarck, we find the Beacon Cafe. The proprietress is Deana Nagle, and she's one of the top bakers in the Prairie states. The cafe is open from 7 AM until 5 PM Monday through Saturday (except in August), and from September through May, the big booths in the back are occupied by the Coffee and Cake Checker Club on Saturday afternoons.
There were a dozen or more members of the club, all but one of them over fifty years of age. Everything was kind of informal, of course, and depending on the weather, the time of year, and so on, attendance would range from four or five to as many as twelve.
Not this Saturday afternoon. Sal had arrived at 1 PM and was the first one to come through the cafe's front door and greet Deana. But ... he was also the only one. It was now 2 PM and Sal was in the big booth in back all by himself.
Sal thought back as he nursed his second cup of coffee. Once, he recalled, it was just him, Dan, and Wayne--- three of them. But never less than that and certainly never just Sal.
He looked over at Deana, stationed as usual behind her counter, and smiled wistfully. "I think I'm it for today," he said.
"Well, Sal," Deana replied, "do remember what day it is."
Sal let out a bit of a sigh. "Of course," he said, "it's the first Saturday in April, isn't it?"
About three years ago, in a previous Beacon Cafe story, we explained about the first Saturday of April and how in Bismarck, it was an unwritten law that if you were a homeowner, you would rake up your yard to get it ready for spring. It didn't matter if there was snow still on the ground, or if it was raining or even snowing. You raked up your yard because that's what you're supposed to do. Failure to comply was the next best thing to a criminal offense.
Sal hadn't even thought about it. Being older, he engaged the services of a nice, enterprising young fellow who took care of yard work for him.
But the rest of the club members thought that doing it yourself was more meritorious and that hiring it out was something like cheating. Sure, Sal thought, they didn't get the raking done in the morning and had to work into the afternoon. That was it. In other years, they had finished earlier, or at least several of them had, and had been able to make it to the club. Today, though, most likely under the watchful eyes of their wives, they were being held to account for performance of this traditional task, and there would be no checkers until the raking was done, all of the dead grass and debris bundled into bags, the tools cleaned and stored, and a subsequent wash-up and change of clothing accomplished.
Sal sighed once more. He thought that at least Louie the Flash, who wasn't married, might have showed up, but perhaps his latest girlfriend was also making him toe the line. And young Blaine, the only member under fifty years old, was likely in Minot helping his parents with the raking (a similar April raking rule held sway throughout most of North Dakota).
"Hey Sal, cheer up, I've got lemon bars today. I know you like those," Deana said.
Sal actually hated lemon bars. His frown must have been visible, because Deana smiled and quickly said, "Hey, I'm just April fooling you. Actually I have apple crumble. Would you like one?"
"Sure would," he replied, "and can you refill my coffee? I think I'll stick around just a little longer."
Sal thought maybe he could read the checker news in this month's issue of the State checker magazine, the Roughrider Checker Bulletin. Sal enjoyed his dish of apple crumble--- Deana had added a scoop of vanilla ice cream and it was delicious--- and had just finished reading about a tournament in Williston, when in came Louie the Flash and Mike!
"Hey, you look pretty lonely back there!" Mike said. "We know it's already after 3 PM but we can still spend an hour together, and I'm sure you have a problem for us."
Sal couldn't hide his big smile. It would be a good Saturday after all. "Done raking?" he asked.
"Yeah," Louie said. "My girlfriend Judy said she wouldn't keep company with a guy that can't even rake his yard when he was supposed to, so I had to get on it. But then about halfway through I went back inside and told her I can't keep company with a girl who keeps a guy away from his checker friends. So we split up on the spot and here I am."
"I ran late this year," Mike said, "but I'm all done, and the wife let me loose for a little while."
"Well then, there's just time enough for this one. It's in the Roughrider magazine. I haven't looked at it yet so how about we all solve it together?"
Deana brought over two mugs of coffee and a couple more dishes of apple crumble. "Here you are boys, better late than never!"
Sal referred to his magazine and laid out this position on one of the checkerboards.
"Let's get started," Sal said. "See if we can solve it in an hour."
Apple crumble, often locally called krumkake is certaily delicious. Unfortunately we can't supply that for you. But you can enjoy the checker problem that Sal and the "boys" are working on. Find the right moves and then don't let your mouse be lonely--- click on Read More to see the solution.[Read More]
Marvin J. Mavin, Captain of the Detroit Doublejumpers, was in Las Vegas. His team had an exhibition match with the Las Vegas Lettuce, one of the top teams in the AAA West Coast League.
The Doublejumper coaches decided the team could do with a little recreation, and gave them the day off before the match. Now, Marvin would have liked to bring along his fiancee, Priscilla Snelson, but as CEO of Rust Belt Holdings it wasn't always possible for her to get time off. So Marvin had the day to himself.
He read a few of those ads that you find in the hotel room magazines, and one of them mentioned a bar and restaurant called "Good Luck 13" that supposedly had craft beers and "the best burgers this side of anywhere."
Good Luck 13 was within easy walking distance of the hotel, so around six in the evening Marvin moseyed on in. He found a clean and tastefully decorated place. There was a long curved bar, and a lot of booths with red leatherette seats. Being by himself Marvin decided to take a chair at the bar. He asked the bartender for a pint of his best local craft beer, and also a menu.
The menu was full of praise for the burgers, of course, and there was a large variety. But the following menu entry caught his eye.
"Good Luck 13 Burger. $39.95. Thirteen three ounce patties with bacon, lettuce, tomato, seven slices of American cheese, Good Luck 13 sauce, and grilled onions. If you like, add $10 to try our 'Good Luck 13' blindfold checker problem, and if you solve it, the burger and the problem are BOTH free."
Kinda like gambling, Marvin thought, but hey, it's Vegas. It would cost him $49.95 if he couldn't get the problem. However, how could he not be able to solve a checker problem? He was a top professional, and top pros play blindfold all the time. Or would it be cheating?
Marvin was a pretty straight shooter, so he told the bartender he was a professional player, and asked if he would still be eligible.
The bartender laughed. "Yeah, everybody knows you, you're Marvin J. Mavin and you're real good, least you think you are. Well, don't matter none. You ain't gonna solve Good Luck 13. Ain't nobody never done it. I'll let ya in on somethin'. The management goes halfsies with me on the extra ten bucks, so I kinda like encourage people. So go for it, make me an extra fiver."
Marvin agreed, although privately he wondered what he was getting himself into. The bartender put in the order for the giant burger, and then showed Marvin a diagram with the following position on it.
"Okay, here's the rules. First, you got one minute to memorize this 'cause it's blindfold, remember? No takin' notes or arranging your french fries or nothing. Then the time limit's an hour, and you have to find 13 different solutions to this problem --- Good Luck 13, get it? Yeah, and different ways of jumping are okay but transpositions ain't. Ha ha, well there it is, bud! Your minute starts now."
The bartender pulled out a stopwatch, set it to zero, and pressed the start button.
"Wait ... wait just a second. Thirteen solutions? You gotta been kidding ... "
"Them's the rules and times-a-running, bud. Better start thinkin'!"
After sixty seconds, the bartender snatched the diagram out of Marvin's hands and announced, "Fifty-nine minutes to go!"
"You said an hour ... "
"An hour total, bud. Ha ha, down to fifty eight fifteen now!"
The burger arrived about ten minutes later, a towering monstrosity of beef patties, cheese, bread, and fixings. But Marvin was deep into the problem.
"Let's see ... that's three ... no, here's another, so four ... thirteen? It has to be a trick of some kind ... "
Now, we can't offer you a free thirteen patty hamburger. You'll have to provide that for yourself. But we can supply you with a chance to solve an unusual and intriguing problem, without risking ten dollars or anything at all. Try to solve it blindfold if you can by just memorizing the diagram and working on it in your head. Otherwise see if you can do it without setting up a board and moving the pieces around. Or move them if you have to.
Spend some time on this and when you've found every solution that you possibly can, click on Read More to see the full suite of solutions and the rest of the story.[Read More]
Pictures at an Exhibition, composed in 1874 by Modest Mussorgsky, was originally a suite of ten piano pieces linked together by a "Promenade" theme, intended to represent the experience of walking through an exhibition of the paintings of artist Viktor Hartmann at the Imperial Academy of Arts in St. Petersburg, Russia. The compositions were orchestrated in 1922 by Maurice Ravel, and this is the version that is most well known today.
We have something similar in checkers, and in this, the 67th Problem Composing Contest sponsored by Bill Salot, we'll see an exhibition of checker art that is visual as well as artistic in play quality. To illustrate this, here is one that Bill calls WreckTangle and credits to former World Champion Alex Moiseyev, who created it independently. However, it happens that Ed Atkinson was the original composer; he called it Pandora's Box.
Bill notes that there are other famous images on a checkerboard, such as the Picture Frame arising from games in Boland's Famous Positions, Page 187. Bill goes on to remark that there are numerous other patterns published in various checker problem books.
In this month's contest, Bill features three "art works" so to speak (alas, not ten as in the original "Pictures at an Exhibition"). They can be found on the contest page. Be sure to try them out and then vote for your favorite.
The solution to WreckTangle (or Pandora's Box, if you will) can be seen (after you've tried to solve it, of course!) by clicking on Read More. We hope you enjoy it and all of the contest problems.[Read More]
March, 1955. The Kilauea volcano in Hawai`i had erupted. But in Bismarck, North Dakota, it was still winter, and the cold and snowy weather just didn't want to let go.
On a Saturday afternoon later in March Sal Westerman, the unofficial leader of the Coffee and Cake Checker Club, looked out of his living room window. It was about 12:45 in the afternoon, and the Club would have its regular Saturday meeting at one o'clock at the Beacon Cafe, the regular venue for the many years the Club had been in existence.
It wasn't looking good out there. The temperature was at about 20 degrees. It could have been a lot worse but the wind was at 25 miles per hour and there was a combination of snow and freezing rain falling. While Sal almost always walked to the Club meetings--- it was usually just a leisurely 10 minute stroll--- this time he didn't think it would be such a good idea. The sidewalks and streets would be treacherous, and he didn't want to take another fall as he had during a previous winter.
Well, he'd ask his wife, Sylvia, for a ride. That was something that she would be happy to help with, as she always worried for his safety (Sal, at 73, wasn't getting any younger). But there was just one little problem.
Sylvia's sister Phoebe was visiting. She had come from Dickinson a few days earlier and wouldn't go home until Tuesday. And Phoebe's goal in life was to make Sal miserable, or at least so it seemed.
Sylvia and Phoebe were at the kitchen table, chatting over a pot of tea. Sal knew what he was getting himself into, but he went into the kitchen and said, "Sylvia, do you think I can get a ride to the Beacon? The weather is awful and ... "
Phoebe interrupted, skipping her usual preliminary throat-clearing. "Can you not see that we are busy chatting? How rude of you to interrupt! And furthermore, you say the weather is awful but you expect your wife to go out driving on such a day? Is it some sort of emergency? Well, speak up, then!"
"My checker club ... "
"Your checker club? Why of all the foolishness." Phoebe looked over at Sylvia. "Sister dear, I thought we had spoken about you forbidding this ... man ... of yours from wasting more of his time on this checker nonsense of his, when he should be helping you with laundry and cleaning and so many other important things." She turned back to Sal. "Checker club, indeed! You can stay at home, where you belong, and do something useful for a change. Now, leave us alone and go wash some windows or something."
Sal addressed Sylvia again. "Syl, I'm going to be late ... "
"What did I just tell you?" Phoebe exclaimed. "How dare you!"
"It's fine, Phoebe, it's fine. I'll be right back." She stood up. "Come on Sal, I'll take you. I don't want you out walking today."
Sal and Sylvia exited the kitchen, leaving Phoebe sputtering into her teacup. About five minutes later, Sylvia stopped in front of the Beacon's entrance at the Provident Life Building.
"Be sure to call for a ride home," Sylvia said as Sal exited the car.
"Thank you, sweetheart," Sal said, "and my regards to your sister."
Sylvia gave Sal a sharp look, and then laughed prior to driving off.
It was already about ten after one, and as Sal entered the Cafe he saw that there was a smaller than usual group gathered in the big booth at the back. Wayne and Dan were there, as were Delmer and Louie the Flash, but that was all.
"Bad weather today," Sal said as he reached the back of the cafe, "must have kept most of the boys away." Sal referred to the members of the Club as the "boys" even though all but one of them were at least 50 years old.
"Well, we're here Sal," said Wayne. "But you're never late, so we wondered what went wrong."
"Phoebe is visiting," Sal said tersely.
"Oh," Dan said, and the rest of the boys quietly nodded their heads. They knew all about Sylvia's sister.
"Well, I'm here now," said Sal, "and I have a nice one from Brian in St. Louis." Brian was a grandmaster problem composer and one of Sal's checker pen-pals.
Sal looked over at Deana, the proprietress of the Beacon, who was stationed as usual behind her counter. "What have you got today?" he asked.
"Double chocolate brownie bars," she said, "just the thing for a winter's day. And lots and lots of fresh hot coffee."
"Well then," Sal said, "here you go." He laid out the following position on one of the checkerboards that the boys had set out.
"I think you boys will be buying today," he added. The tradition was that if the boys could solve the problem Sal would buy the bars, otherwise the boys would.
But as always the boys were already hard at work and didn't reply.
If, wherever you may reside, you experience bad winter weather, we do hope you'll be cautious when out walking or driving. Meanwhile, though, stay indoors and enjoy Brian's problem. A warm mouse click on Read More will of course bring you to the solution and the conclusion of our little story.[Read More]
It's quite early for the Easter Bunny (Easter 2023 is on April 9) and somewhat late for Chinese New Year and the Year of the Rabbit (January 22). So let's look at a little math problem instead:
"Chris is training Hoppity, her pet rabbit, to climb stairs. It will hop up one or two stairs at a time. If a flight of stairs has ten steps, in how many ways can Hoppity hop up the this flight of stairs?"
Oh, wait, this is a checker column. Well, in fact regular contributors Lloyd and Josh Gordon have sent along a "speed" problem they call "Hopper" so it seemed like something about a rabbit would be an appropriate lead-in. And no, the problem has nothing to do with the late GAYP master Millard Hopper.
The problem itself is a lot of fun, and of course the layout of the pieces, not to mention the problem's title, give a huge hint. It's certainly not a hard problem and can be quickly solved with just a bit of visualization. As we're fond of saying, top players will see it at once while the rest of us may require a few more seconds, or maybe even a minute or so.
It doesn't matter what category you may fall in, whether top flight professional or enthusiastic novice. See how fast you solve it and then hop your mouse to Read More to jump to the solution.[Read More]