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Tactics are the most important aspect of the game for chess players of all levels, from beginner to grandmaster.

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Mastering Chess Puzzles: The Comprehensive Guide to Effective Problem Solving

• GM Noël Studer
• Middlegame , Train like a Grandmaster

I often get emails from blog readers who seemingly solve most Chess puzzles correctly but can’t find the right moves during the game.

What is their problem?

Mostly their definition of ‘correct solution’ differs widely from mine.

They either solve Chess puzzles in a way they can’t during a game (try & error), or they are happy finding the first right move and don’t go deeper.

In this article, you will learn why these approaches are so hurtful for your chess progress & how a correct Chess puzzle solution should look.

In the Spotlight: A Chess Puzzle for You

To make a point, let’s look at the following position. If you want to test yourself, take some time to solve the position. Read on once you come up with an answer. (White to move)

The correct answer is 1.Rxf6 Rxf6 2.Rf1 Raf8 3.Qg5 Kg7 4.Nh5+

Other sub-variations work, such as playing 2.Qg5 then 3.Rf1 or playing 4.Bxf6+ first before playing 5.Nh5+.

The key is to finish the calculation once the piece is regained by force.

Any solution not written down until the end is not correct. This might seem nitpicking, but it is actually extremely important.

During a game, you don’t have the benefit of knowing there is a win. You have to calculate clearly and can’t just play the move that looks most tempting. It might very well be that a tempting move loses because of a trick at the end of the line.

To prepare for the in-game moment, we need to calculate correctly and, until the end, also in training.

So if you just thought, “Ah, 1.Rxf6 Rxf6 2.Rf1 wins”, you have some work to do.

Your intuition is right, but sooner than later, there will be an in-game position where your intuition leads you on the wrong path. This is where your crystal clear calculation should come in and save your ass.

Now let’s look at the two most common ways to do it wrong, and you’ll learn how to do it better next time.

Falling into the Trap: The Try & Error Method

This is a phenomenon mostly happening when studying with online tactics trainers. You see a tempting move and execute it. If it is correct, you will do the same on the second move. If it is wrong, you have another shot at the same puzzle and go with the next most likely move.

Eventually, you will “solve” (I’d rather say guess) the puzzle. You might try Bxf6, Rxf6, or Qg5 in any order in the example above. Even if you get 1.Rxf6 right from the get-go, you shouldn’t really be proud. You probably didn’t see until the end of the line, so you didn’t improve any skills that help you in real games.

This is also the reason why I’m not a big fan of speed puzzle solving like Puzzle Rush or Puzzle Racer . The limited time forces you into a try & error mindset, which will be useless during a real game.

The only real solution here is:

Never solve by the try & error method.

It is a horrible habit that increases your confidence (“I got it right”) but worsens your chess. This inevitably leads to way too high expectations and, thus, to disappointment and frustration.

Just remember Try & Error —> Frustration, and you should be able to withstand the temptation.

A Common Mistake: Shallow Thinking and Its Consequences

Shallow thinking is the next biggest issue and is a close friend of the try & error method. Both stem from the same human tendency to be lazy.

It is hard to calculate a line until the end, but sometimes glaringly obvious which first move one should play. So you think, “I’ll just play this move and think from the next position.”

The problem here is a practical one again. Sometimes, the obvious moves are wrong!

When solving tactical exercises, you know there is something good in the position. If there is only one forceful-looking move, you might be tempted to go with it without thinking.

But during the game, this isn’t true at all. There are positions where a move looks good but loses instantly.

That’s why it is important that you only execute a move during training when you finish your full calculation process. This habit will eventually save you a lot of points during your games.

Wisdom from Artur Jussupow

Artur Jussupow, the former World #3 and my Coach in my teenage years, had some great advice when I used the shallow thinking method in training.

A common conversation would go like that:

Artur: “Solve this position, White to move, you get 5 Minutes

Noël (after 30 seconds): “I believe f5 looks good.”

Artur: “You can believe in the church; in chess, we calculate and know.”

He would then not say anything until I came up with the full line I calculated until the very end.

Since then, whenever I thought, “This move looks good,” I was reminded of Artur telling me to finish my calculation before making assumptions.

The Road to Success: How to Solve Chess Puzzles Correctly

Now that you know what to avoid solving a puzzle correctly is pretty straightforward. Open up your puzzle book or go to your favorite Online Chess Tactics Trainer.

Now follow these three simple steps:

1) Carefully examine the position before jumping into one move that looks or feels right (sometimes my students miss that they are material up or down because they immediately try to spot the right move).

2) Come up with a List of Candidate moves. The simplest way to get the most forcing ones it to look for:

in this sequence.

3) Calculate one move at a time. Start with the most forceful one ( if there is a checkmate , you don’t need to calculate other moves!) and finish only with a clear evaluation. If you win by force, shortly make sure you didn’t miss anything, then write down the solution and compare it with the puzzle solution.

If the evaluation isn’t good (enough), continue with the next most forceful move. If none of the initial candidate moves ends in a good (enough) evaluation, you either need to find more candidate moves or decide on the line with the least bad evaluation.

You are now curating a habit that will help you during your exercises but even more in-game. The right, non-rushed thought process helped me and my students save dozens of points. It will do the same for you.

I firmly believe that

anyone can improve their chess through the right mindset and training techniques.

I’m here to guide you on your journey to chess mastery.

Read more about Noël

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Chess and Problem Solving: Sharpening Your Mind

Chess is not just a game; it is an activity that challenges your mind and enhances your problem-solving skills. In this article, we will explore the connection between chess and problem-solving and how playing this strategic game can have a positive impact on sharpening your mind. Whether you are a beginner or an experienced player, understanding the cognitive benefits of chess and incorporating it into your routine can help improve your critical thinking, decision-making, and analytical abilities. So, if you are ready to embark on a journey of mental growth and development, let’s delve into the world of chess and discover how it can boost your problem-solving capabilities.

The Benefits of Chess for Problem Solving

Improves critical thinking skills.

Chess is a game that requires players to think critically and make thoughtful decisions. By analyzing positions and evaluating potential moves, chess players develop their ability to think logically and strategically. This mental exercise helps improve critical thinking skills, enabling individuals to approach problems and challenges in a systematic and analytical manner.

Enhances pattern recognition

Chess is a game of patterns. Successful chess players are adept at recognizing and understanding various patterns on the chessboard. This skill transfers to problem-solving situations outside of the game as well. Through regular chess practice, individuals can enhance their pattern recognition abilities, enabling them to identify similarities and connections in different contexts. This heightened pattern recognition skill can be beneficial in various problem-solving scenarios, such as identifying trends, predicting outcomes, or finding creative solutions.

Fosters strategic planning

Chess is all about strategic planning. Players must consider short-term and long-term goals, formulate and adjust their plans accordingly, and anticipate their opponents’ moves. This constant exercise in strategic thinking fosters a mindset that is crucial for effective problem solving. Chess players learn to weigh different options, anticipate consequences, and develop strategies to overcome obstacles. These skills transfer beyond the chessboard, allowing individuals to approach problem-solving situations with a well-thought-out plan and the ability to adapt and adjust their strategies as needed.

In conclusion, engaging in chess as a means of problem-solving practice offers several benefits. It improves critical thinking skills, enhances pattern recognition abilities, and fosters strategic planning. By incorporating chess into one’s routine, individuals can sharpen their minds and cultivate valuable problem-solving skills that can be applied to various aspects of life.

Developing Problem-Solving Techniques through Chess

Analyzing positions and making decisions.

In the game of chess, players are constantly faced with the challenge of analyzing positions and making crucial decisions. Each move requires careful evaluation of the current situation on the board and the anticipation of potential future moves by the opponent. This process helps develop problem-solving techniques as players are forced to think critically, weigh different options, and assess the consequences of their decisions.

Analyzing positions involves considering various factors such as piece placement, pawn structure, king safety, and potential threats. By carefully assessing these elements, players can identify advantageous moves that can lead to a stronger position or material gain. This analytical thinking translates into real-life problem-solving skills by encouraging individuals to break down complex problems into smaller components and evaluate different approaches.

Identifying and solving chess problems

Chess is not just about playing against human opponents; it also offers a wealth of puzzles and problems that require critical thinking to solve. Chess problems can be in the form of tactical puzzles, where players need to find a sequence of moves to gain a significant advantage or checkmate the opponent’s king. Solving these problems enhances problem-solving abilities by challenging players to think creatively, consider alternative solutions, and anticipate potential obstacles.

Identifying chess problems involves recognizing patterns, calculating moves, and visualizing potential outcomes. This process trains the mind to look for hidden opportunities and consider unconventional strategies. By honing these skills in chess, individuals can apply them to real-life situations, improving their ability to identify problems, devise efficient solutions, and adapt their approach as needed.

Learning from mistakes and adapting strategies

Chess is a game of continuous learning, and making mistakes is an inevitable part of the process. However, what sets successful chess players apart is their ability to learn from these mistakes and adapt their strategies accordingly. Analyzing past games, reviewing critical positions, and understanding the reasons behind errors are crucial steps in improving problem-solving techniques.

By reflecting on their mistakes, chess players develop a growth mindset that emphasizes learning and improvement. They learn to identify weaknesses in their thinking process, detect recurring patterns of errors, and adjust their strategies to avoid similar pitfalls in the future. This adaptive thinking nurtures problem-solving skills by encouraging individuals to approach challenges with resilience, flexibility, and a willingness to reassess their approach when necessary.

Overall, chess serves as an excellent platform for developing problem-solving techniques. Through analyzing positions, solving chess problems, and learning from mistakes, players sharpen their minds and acquire valuable problem-solving skills that can be applied to various aspects of life.

Chess Tactics and Problem-Solving

Understanding tactical patterns.

In the game of chess, tactical patterns are essential for success. These patterns are specific combinations of moves that players can use to gain an advantage over their opponents. Understanding these patterns allows players to identify opportunities and make strategic decisions accordingly. Some common tactical patterns include forks, pins, skewers, and discovered attacks. By studying and recognizing these patterns, players can improve their problem-solving skills and make better moves on the chessboard.

Applying tactical knowledge in problem-solving

Chess is not just a game of strategy; it also requires problem-solving skills. Players must analyze the position, evaluate potential moves, and anticipate their opponent’s responses. By applying tactical knowledge acquired through studying patterns, players can effectively solve problems on the chessboard. They can identify weaknesses in their opponent’s position, find winning combinations, and create threats that force their opponent into unfavorable situations. Problem-solving in chess requires a combination of logical thinking, creativity, and the ability to calculate multiple moves ahead.

Utilizing chess puzzles for practice

Chess puzzles are an excellent tool for practicing and sharpening problem-solving skills. These puzzles present players with specific board positions and challenges them to find the best move or sequence of moves. By regularly solving chess puzzles, players can improve their tactical awareness, pattern recognition, and overall problem-solving abilities. Chess puzzles come in various difficulty levels, allowing players to gradually progress and challenge themselves. Additionally, solving puzzles can be an enjoyable and engaging way to enhance one’s chess skills outside of actual gameplay.

By understanding tactical patterns, applying tactical knowledge in problem-solving, and utilizing chess puzzles for practice, players can sharpen their minds and improve their overall chess gameplay. Developing strong problem-solving skills in chess not only enhances one’s performance on the board but also translates into improved critical thinking and decision-making abilities in various aspects of life.

In conclusion, chess is not just a game of strategy and competition; it is also a powerful tool for enhancing problem-solving skills and sharpening the mind. Whether you are a beginner or a seasoned player, engaging in regular chess practice can improve your critical thinking abilities, decision-making skills, and overall mental agility. By analyzing complex positions, evaluating multiple possibilities, and devising effective plans, chess players develop a unique mindset that can be applied to various real-life situations. So, if you are looking for a fun and challenging way to boost your cognitive abilities, consider immersing yourself in the world of chess. Start honing your problem-solving skills today and witness the positive impact it can have on your mind.

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Home » Chess Strategy » How To Solve Chess Puzzles (Quickly and Easily) For Beginners

How To Solve Chess Puzzles (Quickly and Easily) For Beginners

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Which puzzles should you solve?

• Look for forcing moves
• Look at what each piece is doing
• Look for what would be left after
• Practical Examples on Solving Puzzles
• Types of Puzzles
• Art of Solving Puzzles

If you’re new to the game this is the question you’ll face especially during your training. So in this article, I’ll share a simple 3-step process you can use to solve puzzles.

After that, I’ll share some typical examples where we’ll use the process to solve the puzzles and show a way to improve your speed at solving them. Before we move on, I must confess that everyone has a different process. Also with time and experience, the process evolves.

But regardless of that, it’s important to solve puzzles as it improves your tactics and calculation.

Last Updated: September 28th, 2021

At first, you should start with easy puzzles and move on to more difficult ones. Imagine you’ve decided to run a marathon. Is it possible that from day one you’d be able to run 42 kms all at once?

For most humans, that would be impossible. You’d need to train for smaller distances, become better at it and then gradually increase the difficulty.

If you start with the goal to run 42 kms at once in the first few weeks without proper training, you are going to put yourself under immense pressure and become demotivated when you don’t hit your target.

The same also applies when you train in chess. You first start to solve simple chess positions, before you move on to more complex ones.

So if you’re a beginner and have never solved a puzzle in your life, I recommend you start by solving basic ‘Mate in 1’ puzzles first. Once you master that, then you can start with ‘Mate in 2’ puzzles and so on.

You keep increasing the difficulty as things become easier.

Process To Solve Puzzles

• Look for forcing moves.
• Look at what each piece is doing.
• Look at what would be left at the end.

For most masters, because of continuous training, they are able to spot simple combinations and checkmates rather quickly.

While everyone develops their own individual style for solving puzzles, there are some common elements which they all follow.

I’ll share them below.

1) Always look for forcing moves

These are moves where your opponent is FORCED to react to in a certain way. This limits their choices and gives your calculation a direction to follow.

The forcing moves are:

• Checks – Thanks to the rules of the games, a player has to deal with a king in check, and any other move which doesn’t address this problem is illegal.
• Captures – When you capture material, the opponent needs to recapture it back or else they’ll be behind in material. While capture isn’t as forcing as a check, the opponent’s choice is still restricted.
• Attacking moves – What’s your first instinct when someone attacks your queen? Do you ignore it or you make sure that your queen is safe? Under normal circumstances, any player would move their queen away(unless you’re Mikhail Tal!). So basically when you attack something, your opponent has to respond to your threat. Once again, this puts a limit on their number of options.

Now let’s see practical examples and understand how to put these principles into action.

2) Watch out for which piece is doing what

Often there will be a piece that will be performing an important defensive task. Other times, they might be controlling an important square or attacking something. You don’t need to be very detailed on this, but it’s good to have a general understanding of what pieces are doing.

As you become more experienced, this process happens unconsciously without your active interference.

3) What are you left with at the end?

These three things will serve you as a good starting point.

Now let’s get down to business and see how it all works in practice.

Types of Puzzles and How To Solve Them

Let’s go over the different types of puzzles and how to solve them, beginning with Mate in One Puzzles. We’ll keep increasing the difficulty.

How To Solve Mate in One Puzzles

In these puzzles, you’re supposed to deliver a mate in 1 move. This means here, you should always look for the checks in the position, since that’s the only way you could deliver a checkmate.

Black to play.

Let’s ask ourselves – “What are the forcing moves they can play?” We can notice they have 2 checks at their disposal –

1…f2+

1…Re1+

Since this is a mate in 1 puzzle, one of them should lead to a checkmate. Let’s just find that out with a simple calculation.

After 1…f2 , White can still play 2.Kf1 or Kh1 and it’s not a mate yet.

And after 1… Re1+ , can the White king move anywhere? Absolutely not! So after the 2nd move, White is checkmated. Therefore the solution would be 1…Re1# .

This is a simple illustration to show you how a more complicated process works.

How To Solve Mate in Two Puzzles

It’s White to play and mate in two in this position. What to play?

Let’s start by calculating the forcing moves in the position. What are the checks White has? We immediately noticed one 1.Rd8+!   How can Black respond to it?

They’re forced to play 1…Rxd8 .  Again, we ask ourselves, what are the forcing moves White has after 1…Rxd8 ? If you notice carefully, the queen and bishop are eyeing the long h1-a8 diagonal and will soon deliver a checkmate.

So we can find White has 2 checks, and apparently both lead to a checkmate after 2.Qa8# or 2.Qb7#

Another similar example on mate in two moves.

Put the process that you learned to use above, and you should be able to find an answer.

White plays –

1.Rxe8+ and after 1…Rxe8 2.Qxg7#

After 1…Qxe8 also 2.Qxg7# .

White is winning after Rxe8+ .

Here, I’d also like to emphasize here on the importance of paying attention to the details in the position. If you notice, White is attacking on the g7-point. They could’ve started with  1.Qxg7 or 1.Bxg7, but in both cases, the knight was defending the g7-pawn.

So after 1.Rxe8 , we eliminate the knight on e8 defending the g7-pawn. During your calculation, pay attention to such small details. They help you understand the position better.

General Tactics Puzzles

Black has just played …Nd4 . How should White respond?

Let’s kick off our calculation by looking for forcing moves. White could give a check with 1.Bb5+. Black would then play 1…Nxb5 capturing White’s bishop. Sounds like a bad deal!

So continue looking for other options.

Do you have any captures? Yes, we can spot 1.Nxd4 . What would Black do then? Let’s calculate one by one.

They could play 1…exd4 , but then we capture their bishop with 2.Bxg4. Now if we count the pieces, we are a piece up! So this is a bad deal for our opponent, and they shouldn’t take it!

What else could they play? 1…Bxe2 was another option for them.

Now again we have 3 options – 3 forcing moves – 2.Kxe2, 2.Qxe2, 2.Nxe2 .

Now, it’s easy to discard 2.Kxe2 because Black then has 2…exd4 and the material is equal. We lost a knight and bishop, and so did our opponent.

If you observe on 2.Qxe2 , Black has the same reply – 2…exd4 . We could play 3.Qb5+ and try to gain the b7-pawn.

But before we move there, let’s examine another important option we might have – 2.Nxe2 . Suddenly, we realize that Black has no …exd4 . Our knight is safe, and we have lost only 1 bishop, while our opponent has 2 pieces, the bishop and the knight. We are a piece up!

And so we’ve established that 1.Nxd4 Bxe2 2.Nxe2! leaves us with an extra piece.

A Famous Position

This is a popular position.

Here White has a strong way to proceed. Can you spot how?  Let’s get down to business!

What are White’s forcing moves?

1. Bxf7+ (check)

1. Nxe5 (capture)

1. g4 (attacking move)Very quickly we can find out that 1.Bxf7+ Bxf7 brings nothing. White loses their piece and there doesn’t seem to be a reasonable follow up.So let’s have a look at 1.Nxe5 . Black has 3 choices then. Here’s how the process could look like – 1…dxe5 2.Qxh5 (capture) and White wins a piece.

Another line could run like 1.Nxe5 Bxd1 2.Bxf7+ (check) Ke7 3.Nd5# (check). A beautiful mate!

1.Nxe5 and now let’s consider 1…Nxe5. White plays 2.Qxh5 (If instead 2.Bxf7+ , Black defends with 2…Bxf7 after which White has nothing.) 2…Nxc4 .

Looks like White has lost a piece, but they have a forcing move left at their disposal 3.Qb5+! Qd7 4.Qxc4 and White regains the piece and has an extra pawn.  Now we know that 1.Nxe5 works and leaves us with an extra pawn!

If you calculate for 1.g4 , you’ll see that it leaves us with nothing after 1… Bg6 .

So what do we play? We go for 1.Nxe5! Because it leaves us with extra material compared to the other two lines.

Pattern Recognition — The Art of Solving Puzzles… Faster!

Have you ever wondered how a Super Grandmaster like Hikaru Nakamura is able to solve positions at such a fast speed? That’s because he has solved many positions over and over that have built up his ‘pattern recognition muscle’. For a lot of master level players and strong amateurs, this thing holds true.

The easiest way to build this muscle is to solve puzzles on one theme!

It’s like to make your legs strong, you focus only on that muscle group and do squats daily.

Similarly, to become good at pins, you solve puzzles whose main theme is a pin.

Enough of talking, let me show you how it actually works.

How Pattern Recognition “Fires Up” Old Memories of Training

Let me share two puzzles to show how effective this tool can be.

It’s White to play, what would you play? Let’s use the process and examine the forcing moves – 1.Nh6+, 1.Ng5+, 1.Nd8+, 1.Ne5+, 1.Nxd6+ .

You’ll notice that after all other moves apart from 1.Nh6+ , White is losing their queen with 1…Nxd5. So immediately all those options are discarded.

Let’s examine 1.Nh6+ (double check with queen and knight). Black’s only legal move is to move the King away with 1…Kh8 . Then again we have two checks –

On 2.Nf7+ , Black plays 2…Kg8 while repeating the position. So does White have any other options?

2.Qg8+ looks crazy, but let’s keep going with that fantasy. Black has only one forced move 2…Rxg8+ and then suddenly we spot that the only forcing move leads to a checkmate – 3.Nf7#.

So we instantly play the solution – 1.Nh6+ Kh8 2.Qg8+ Rxg8 3.Nf7# .

This pattern is also known as the smothered mate .

Now that you know the previous puzzle, this one should be easy to solve. How would you continue as White?

On careful inspection, you’ll see that the first move is 1.Qb3+. Now consider Black’s options 1…Rf7 and 1…Kh8.

After 1…Rf7, White White’s forcing moves are 2.Qxf7, 2.Qxb7 .

In both cases, White achieves nothing .

So what do we do? We return to the position and find out if there’s anything else.

Suddenly, we can spot an attacking move with 2.Ng5. Black’s rook is pinned and it soon will be captured.

So – 1.Qb3+ Rf7 2.Ng5 leaves us with an extra exchange as we will capture the f7-rook with our knight.

After 1.Qb3+ Kh8 , our forcing moves with a check (2.Qxb7 and 2.Qg8+) bring us nothing, so we play something else. What’s that? We can play 2.Ng5!

Can you spot the similarities between this position and the previous one? That’s basically how pattern recognition works in chess. You find something you are familiar with and try to execute that on the board.

If you notice carefully, Black has no way to defend against 2.Nf7+ or 2.Ne6, leaving White with an extra exchange. And thanks to the last puzzle, you should be able to figure out how White threatens a smothered mate.

So the solution will be 1.Qb3 Kh8 2.Ng5! 

To become better at solving puzzles, there’s only one way and that is by solving them everyday. This is also how you’ll build your muscle for pattern recognition.

The process shared here should give you a good starting point. Go to chess.com or lichess and start to put what you learnt here into practice!

Happy solving!

I hope this guide on how to solve Chess puzzles helped you. You may also be interested in reading about castling in Chess . and the list of ways on how to get better at Chess .

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10 best british chess players, ranveer mohite.

Ranveer Mohite is a professional chess player from India. His current elo rating is 2277, and he regularly writes about chess, expressing his passion for the game. Check out his blog here. Connect with him on LinkedIn.

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Dark Doings problems – Part 1

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The name Dark Doings refers to composed problems in which the white force consists solely of the king and one other unit (if any), while Black possesses the full set of sixteen pieces. This maximum contrast in materials creates arresting diagram positions, and there’s a certain wit about such problems that seem to depict White prevailing against overwhelming odds. The Hungarian composer Ottó Bláthy originated the term Dark Doings in a 1922 Chess Amateur article, which includes many of his own renditions of the scheme. Some of these compositions have become classics, such as his oft-quoted mate-in-16 and mate-in-12 . In the century since, problemists have continued to employ this special form of material to express a variety of themes in different genres. Here we shall look at a number of outstanding orthodox examples.

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How (and why) to play online chess in Microsoft Edge

Did you know that the game of chess has been around for over 1,500 years? As one of the oldest and most widespread games, chess has been the foundation of countless theories, combinations of play, and tournaments between global competitors and computer programs alike.

Learn how to play this fascinating game in Microsoft Edge , take on an AI opponent of varying difficulties, and hone your cognitive and strategic thinking skills—all while partaking in a grand gaming tradition.

Play chess online with Microsoft Edge’s Games menu

When you select the Games menu in the Microsoft Edge sidebar, you’ll unlock thousands of staff-recommended games that you can play to your heart’s delight, including free online chess. Accessing the Games menu is easy. On the right side of the Microsoft Edge browser, look for the Games icon, which resembles a pair of black and purple chess pieces. If you can’t find the Games icon, select + at the bottom of the sidebar and add it in the Apps section.

Online chess games that you can play for free

Once you search chess in the Games search box, you’ll find Master Chess : the official chess game from Microsoft. When you select Play , it will open directly in a Microsoft Edge tab. Choose to go up against an AI opponent at varying levels of difficulty or real players from all over the world. Learn the rules and moves for each chess piece, and take your game further by getting tips and tricks for how to win in fewer moves. You can even make gameplay into an ongoing learning experience by playing this in-browser chess game while jotting down insights via OneNote in the Edge sidebar.

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Why should you play online chess?

Chess is not just one of the oldest and most beloved board games in the world; it’s also one of the most studied. Researchers have analyzed the intellectual challenge that chess presents both to amateurs and grandmasters alike, and they found the following cognitive benefits:

• Prediction and anticipation. Anticipating your opponent’s next move is vital to being successful in chess. Not only do you need to anticipate the immediate next move, but expert players have been able to anticipate as many as ten approaching moves, even predicting how the game might end.
• Memory improvement. Memorizing combinations of moves and their potential outcomes is a key chess strategy. By remembering the moves that you and your opponent have already made, you can also sort out what pieces to use or sacrifice in your next moves. Plus, you might even recognize the moves of a famous tournament game that you can replicate.
• Greater flow state. Flow state may be best known as a phenomenon where players, athletes, and performers who are under immense pressure reach their peak performance. They’re able to focus entirely on the game or performance and eliminate all distractions. You don’t have to be a professional athlete or performer to reach flow! You might experience it when you’re deep in a chess game, too.
• Creative problem-solving. In playing chess, you can surprise your opponent with a well-executed series of moves. Not only are you solving the problem of, say, protecting your king or an important piece, but you can also do so in a way that catches your opponent off guard.
• Protection against dementia. Studies have shown that chess is a proven factor in reducing the chances or symptoms of dementia ² . This is because the complex mental functions of chess engage the brain in healthy ways, which can also improve memory, calculation, visual-spatial skills, and critical thinking abilities.

Xbox integration with Microsoft Edge

There’s so much more you can play in Microsoft Edge. In addition to all of the free games available in the sidebar Games menu, Microsoft Edge is also tailor-made for online gaming with Xbox integration. You can play the latest blockbuster games with Xbox Cloud Gaming ¹  and connect your account to your console for the ultimate online experience. These are just a few reasons Microsoft Edge is the best browser for gaming .

If you’ve never played chess before or you haven’t played in ages, take heart: you can get started right in your Microsoft Edge browser, for free! Try Microsoft Edge today , and rediscover this classic game.

• [1] Requires Xbox Game Pass Ultimate subscription and supported controller (both sold separately)
• [2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6617066/

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More From Forbes

5 keys to solving the right problems in your business.

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Two multi-ethnic workers working in a plastics factory, standing on the factory floor, looking at ... [+] the control panel of one of the machines. The African-American man is pointing to the panel. His coworker, an Hispanic woman, is holding a digital tablet.

There is no doubt that today’s business challenges are more complex and global than ever, but I still see my peers and business leaders using the same strategies that worked for them years ago. Aspiring new business owners often sink millions into innovations and marketing plans that never get off the ground, and overlook simple details that cost them time, energy, and success.

For example, many businesses are currently struggling with getting their employees back to the office for work, to improve business productivity, accountability, and customer satisfaction. In fact, this challenge clearly has personal team considerations, as well as business implications. Many people prefer the flexibility and comfort of working from home, outweighing results and growth.

I’m not sure if the real problem here is business process or people management, or both, but there is certainly much room for error on both sides. As a consultant, I found some good strategies for not solving the wrong problem in a recent book, “ Solve the Real Problem ,” by Roger L. Firestien, PhD., from Buffalo State University, Innovation Resources, and other roles.

He has real credentials in academia, as well as problem-solving and innovation experiences with many businesses around the world. He offers some key recommendations that I also espouse for how to zero in on the root challenge and not waste large amounts of time and money you cannot afford:

1. Creative questions are key to problem definition. Focus on chains of fact-finding questions and judgement or decision questions to bring out solution ideas. In all cases, defer judgment and avoid excuses like “I don’t have time.” One good question can generate whole new fields of inquiry and can prompt changes in entrenched thinking.

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Creative questions are also useful for exploring new business ideas. Just remember that solving customer problems is the challenge here, rather than internal problems. The process and the results are the same – starting with creative questions to find the real opportunity.

2. Adopt a more effective problem-solving mindset. Analyze your habitual approach to problem solving and be prepared to challenge your own assumptions. Avoid settling for symptoms as the problem or jumping to conclusions based on poor information or your own biases. Sometimes we get in our own way and end up working on the wrong thing.

This strategy also applies to new opportunities for customer growth as well as organizational problems. I still see too many technologists whose mindset is focused on the beauty of their innovation, rather than the problem it solves for customers.

3. Don’t trust or act on your first impression. We all make wrong judgments on first impressions, especially with recurring problems or with people who are of a different nationality, race, and ethnicity. First impressions are usually wrong, especially if they are made in an emotional environment, under time constraints, or with too little information.

4. Get an outside perspective with no agenda. The best way to get an outside perspective is to tap into people who run in circles different from your own. Look for “creative catalysts” who can provide a fresh perspective on the problem and potential solutions. Beware of experts in the relevant technology who may have their own biases.

5. Look for the bigger picture, not minutiae. Make sure that you don’t become unable to see the “forest for the trees” by looking only at a few details of the problem. Consciously step back and take a broader view of the challenge ahead. This approach also builds alignment with related perspectives and issues, and results in better long-term solutions.

In the real world, my experience is that none of these strategies will work without conscientious business leadership, committed team members, a positive business model, and a viable customer opportunity. Your team also needs the creativity skills and training to properly diagnose problems and challenges, generate solutions, and put these solutions into action.

I encourage all of you to recognize that every business in today’s world will encounter challenges and world-class problems. Thus it behooves all of us to continuously update our business problem-solving strategies, support a culture of innovation, and keep moving forward in your quest to make the world a better place, and enjoy the journey to get there.

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Chess Problems For Beginners – Solve With Ease

In the world of chess, solving problems is an essential skill that every beginner should develop. Chess problems, also known as puzzles or tactics, are specially designed positions or scenarios that challenge players to find the best moves or combinations. These problems serve a crucial purpose in helping beginners enhance their chess skills and improve their overall gameplay. By solving chess problems, beginners can sharpen their tactical thinking, develop strategic awareness, and gain a deeper understanding of the game.

Types of Chess Problems for Beginners

When it comes to chess problems for beginners, there are several types that can help them gradually build their skills. Checkmate-in-One puzzles are great for learning the fundamental checkmating patterns and practicing basic tactics. Tactics and combinations puzzles offer more complex scenarios that require players to identify winning moves in a given position. Endgame puzzles focus on endgame principles and allow beginners to learn how to convert advantages into victory. Opening traps and pitfalls puzzles help beginners avoid common mistakes and blunders that can occur in the opening phase of the game.

Benefits of Solving Chess Problems for Beginners

There are numerous benefits that beginners can reap from solving chess problems. Firstly, it improves their tactical and strategic thinking. By regularly engaging with puzzles, beginners learn to spot patterns, calculate moves, and anticipate potential threats. Secondly, solving chess problems enhances pattern recognition skills. It trains beginners to quickly identify recurring motifs and formulate effective strategies based on previous experiences. Additionally, chess problems assist in developing problem-solving abilities, which can be applied not only in chess but in various aspects of life. Lastly, solving chess problems increases the overall chess knowledge and understanding of beginners, as they gain exposure to different types of positions, strategies, and ideas.

How to Approach Chess Problems as a Beginner

For beginners, it’s important to approach chess problems in a structured manner. Start with simple puzzles and gradually progress to more challenging ones. Focus on understanding the principles behind the moves rather than memorizing solutions. Utilize books, online resources, and chess apps that offer a wide range of puzzles for practice. Analyze and learn from your mistakes, as they play a crucial role in improving your problem-solving skills.

Recommended Resources for Beginners to Solve Chess Problems

When it comes to finding resources for solving chess problems, beginners have various options. Chess problem books for beginners are readily available and provide a comprehensive collection of puzzles to work on. Online chess websites and applications offer interactive puzzles where beginners can practice their skills against a digital opponent. Chess courses often include exercises and puzzles to aid in the learning process.

Common Mistakes to Avoid when Solving Chess Problems as a Beginner

While solving chess problems, beginners may fall into some common pitfalls. One mistake to avoid is rushing and not thinking through all the possibilities. Take your time to analyze the position and consider different moves. Another mistake is focusing solely on material gain instead of evaluating the overall position. Sometimes sacrificing material can lead to a more favorable outcome. Neglecting the importance of visualization and calculation can also hinder progress. Improve your visualization skills by mentally playing out different moves and variations. Lastly, don’t ignore the solutions and explanations provided with the puzzles. They offer valuable insights and help deepen your understanding.

Tips for Improving Chess Problem Solving Skills

If you’re looking to enhance your chess problem-solving skills as a beginner, here are some helpful tips. Study and analyze famous chess problem compositions to gain inspiration and learn from the best. Regularly participate in chess problem-solving competitions to challenge yourself against fellow enthusiasts. Seek guidance from experienced chess players or coaches who can provide personalized advice and assistance. Lastly, practice solving puzzles daily to maintain consistency and continuously improve your problem-solving abilities.

Solving chess problems is a valuable activity for beginners that offers numerous benefits. By engaging with different types of puzzles, beginners can develop their tactical and strategic thinking, enhance their pattern recognition skills, and improve their overall chess knowledge. It is important to approach chess problems with a structured mindset, utilize recommended resources, and avoid common mistakes. By following these guidelines and practicing regularly, beginners can solve chess problems with ease and pave the way for success in their chess journey.

Doug Barlow

Chelyshkov wavelet method for solving multidimensional variable order fractional optimal control problem

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• Published: 29 April 2024

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• Akanksha Singh 1 ,
• Ankur Kanaujiya 1 &
• Jugal Mohapatra   ORCID: orcid.org/0000-0001-5118-3933 1  

This work presents an effective numerical approach to solving variable-order multi-dimensional fractional optimal control problems. Utilizing well-known formulas such as the variable-order Caputo derivative and variable-order Riemann–Liouville integral, we determine the variable-order operational matrices and product operational matrices for the fractional Chelyshkov wavelet. By using the operational matrices, the process of solving the variable-order multi-dimensional fractional optimal control problem is simplified to a system of algebraic equations. Finally, using the Lagrange multiplier technique, we obtain the approximate cost function based on determining the state and control functions. We establish the convergence analysis and error bounds for the proposed method. To check the veracity of the presented method, we solve some numerical examples.

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Acknowledgements

The “University Grants Commission (UGC)" fellowship scheme provided financial support with NTA Ref. No. 201610127052 is gratefully acknowledged by the first author.

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Akanksha Singh, Ankur Kanaujiya & Jugal Mohapatra

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Singh, A., Kanaujiya, A. & Mohapatra, J. Chelyshkov wavelet method for solving multidimensional variable order fractional optimal control problem. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02083-7

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Revised : 02 April 2024

Accepted : 04 April 2024

Published : 29 April 2024

DOI : https://doi.org/10.1007/s12190-024-02083-7

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• Fractional Chelyshkov wavelets
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Title: accurate adaptive deep learning method for solving elliptic problems.

Abstract: Deep learning method is of great importance in solving partial differential equations. In this paper, inspired by the failure-informed idea proposed by Gao this http URL . (SIAM Journal on Scientific Computing 45(4)(2023)) and as an improvement, a new accurate adaptive deep learning method is proposed for solving elliptic problems, including the interface problems and the convection-dominated problems. Based on the failure probability framework, the piece-wise uniform distribution is used to approximate the optimal proposal distribution and an kernel-based method is proposed for efficient sampling. Together with the improved Levenberg-Marquardt optimization method, the proposed adaptive deep learning method shows great potential in improving solution accuracy. Numerical tests on the elliptic problems without interface conditions, on the elliptic interface problem, and on the convection-dominated problems demonstrate the effectiveness of the proposed method, as it reduces the relative errors by a factor varying from $10^2$ to $10^4$ for different cases.

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