Learning to Play Minesweeper

A Lesson in Deductive Reasoning

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Reasoning allows us to have an accurate understanding of the world.

Correct deductive reasoning allows us to make conclusions that are true, if our initial beliefs and theories are correct.

Inductive reasoning (the scientific method) allows us to have a high probability that our initial beliefs and theories are correct.

Deductive reasoning and inductive reasoning work together.

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Deductive reasoning is a skill that can be improved with practice.

As you practice you will get quicker and make less mistakes.

By improving your deductive reasoning skills you can solve many problems with better results and in a shorter time.

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Why Learn Minesweeper?

• Minesweeper is a game that can help your logical accuracy and speed.

• Minesweeper is mostly “content-free”, meaning that it can help you develop better deductive reasoning skills without having to have a large pre-existing knowledge base.

• Similar logical skills are used in technology troubleshooting and medical diagnoses.

• By improving your deductive skills, you will get a more intuitive feel for how the computer behaves.

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What Minesweeper Teaches

By playing the full game of minesweeper you will• learn to make hypotheses and later test those

hypotheses.• learn how a wrong initial hypothesis will cause

future wrong hypotheses.• learn “if, then, else” logic in you head.• learn to recognize patterns.• learn to filter out which information is relevant

and not relevant to solve the problem at hand.Go

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How You Will Learn

This edutainment game uses several strategies espoused by BrainSMART ® which can help you learn more efficiently and effectively. These include:•This is a simulator of a real game, showing you a game that was previously won, and how it was won.•By using a game simulator structure , it will help you have a low stress state that offers a challenge.•The game should be able to be completed in less than 20 minutes, which is within most people’s attention spans.•The game simulator will use a process of scaffolding, where it will help you build to being able to play the game on your own.•Having diagrams and graphics on the left side and written text on the right improves how our left and right brains process the information.•If you don’t understand something fully, make sure you click the “Go Back” button before continuing too far. The rules to Minesweeper are simple, but not always easy at first.

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What You See When You First Start

This is the start of the game. The grid shows you all 81 squares that exist in beginner mode. 10 of these squares contain a mine (bomb), the other 71 squares are safe. Your goal is to left click on all the safe squares, and avoid left clicking any of the squares that contain a bomb.

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Your First Move

When you first start, you will have no idea about which squares contain a bomb, and which ones are safe. So when you first click, you pretty much do it randomly. The good news is that you have over an 85% chance of clicking on a safe square. For this simulation, click on the square under the magnifying glass.

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Starting the Logic

You were lucky on your first guess. Now, luck stops, and logic starts. From this point forward, if you do the right thinking, and the right moves, you should nearly always win.

But to use the logic you need to understand what the numbers mean.

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Seeing Numbers

You now have a group of squares that are no longer beveled upwards. Some of these contain numbers, and some are blank. All of these squares are safe including those with numbers.

The squares that are still beveled upwards are still unknown. They may be safe, or they may contain a bomb.

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What the Numbers Mean

The numbers in the squares are very important. Each number gives you a clue to where there might or might not be a bomb. But you must understand what the clues mean!

The number tells you exactly how many bombs are neighbors to that square.

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An Example of a Number

Let’s focus on just one of the numbers right now and see what it means.

Look at the 1 that the magnifying glass is on. This is telling us that there is only one bomb that is a neighbor to that square.

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Here is a Zoomed In Picture

We are going to Answer:

Which Squares are known?

Which Squares are unknown?

What is in the central square?

What does that mean?

Are the other numbers important at the moment?

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Squares that are Neighbors to a Number

There are a total of eight squares that are the neighbors of a number, some of these eight are unknown still, and some of them you have found to be safe.

The magnifying glass is showing those eight squares.

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Beveled Squares Around a Number

Of the eight squares that are neighbors to this 1, only the five that are beveled are still unknown about whether they contain a bomb or not.

This means that if you were to randomly click one of those, you would have a one out of five chance of hitting a bomb. This may sound like good odds, but we can do better!

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Finding a Better Numbered Square to Start With

To consistently win the game, you need to find a square that you are 100% sure will not contain a bomb. This is called deductive reasoning.

But to do this, we must first find a square that we are 100% sure IS a bomb.

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Looking For Corners and 1s

Lets look at a different numbered square that might be a better clue.

Squares that contain the number 1 in the outside corner of a group of unknown squares are a good place to start. In this game there are four of these spots.

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Honing In On a Good Starting Square

To understand why squares in the corners are good starting places, we will look at an individual one, and see what it means.

The 1 means there is only 1 bomb that is a neighbor to that square. In the case of a corner, there is only 1 unknown square, so it MUST be a bomb.

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Let’s Focus on this Square

Try to Answer:

What does the center square tell us?

Is one of its neighbors a bomb?

If so, which one?

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Don’t Left Click the Square

While logic tells us that the square with the magnifying glass must be a bomb, at this point you can only hypothesize that the square is a bomb.

You can do this hypothesis by clicking the RIGHT mouse button on top of the square. This will place a flag on that square.

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Pretending We Are Right Clicking

In this simulator we can not actually click the right mouse button. But we will pretend to do this, by clicking on the right button on the mouse on this screen:

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What the Flag Means

After you right click on the square, a flag will appear. This means you think there is a bomb there.

If you are using correct logic then there really is a bomb there. If you’re logic is wrong, then there isn’t, and it will mess up the rest of your logic. (The good news is that our logic is good so far!)

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Let’s Focus on a Different Square Now

We Will Answer:

What does the center square tell us?

Is one of its neighbors a bomb?

If so, which one?

Are there any unknown beveled squares that are safe?

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Now that We Know Where a Bomb Is,Let’s Find Out Where One Isn’t

The numbers can tell us where bombs are. If we use deductive reasoning, they can also tell us where the bombs aren’t.

Lets look at another 1 on the board. We know that this tells us that there is only one bomb as a neighbor. But because of our last move, we now know where that bomb is. (Where the flag is)

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Guessing a Safe Square

Since we have already found the 1 bomb that surrounds this square, this means that any other unknown squares neighboring the 1 must be safe.

Click on the known safe square that the magnifying glass is showing you to continue.

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Good Job, Let’s Try Another

That square was safe, and says there is 1 bomb next to it. There are currently 3 beveled squares that are its neighbors, and one of them is the bomb we found earlier, so both of the other neighboring squares must be safe.

Click on the one the magnifying glass moves to and we will see if it really is safe.

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Keep Going

We found a safe square again, and once again it tells us that there is 1 bomb neighboring it. And once again, we still know which one is that bomb. So we know all the other squares around it are safe.

Click on the one the magnifying glass moves to and we will make sure it is safe.

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You Cleared a Few

That click cleared several spots, leaving us with a lone beveled square that is a bomb.

We can tell it is a bomb, because the squares with a 1 next to it only have it as an unknown. And the squares with the number 2 only have it and the other known bomb as neighbors.

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Pretend Again to Right Click

This simulation still doesn’t have the right click working, so once again, click on the right side of the mouse picture to pretend to right click on the magnifying glass:

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Now That We Flagged That Square, Let’s Find Another

We will keep doing the corner strategy to flag bombs. We need to pretend to right click again, to flag the bomb where the magnifying glass is.

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Can You Find a Safe Square?

There are actually several safe squares next to the 1 that the magnifying glass is on.

See if you can click on one of the safe squares. (If you click one of them, we will click the other two for you.)

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Which One Should Be Flagged Now?

Now that we cleared those squares, we are at a point where we can find another bomb based upon what we just did.

Click where you think the bomb is. (Remember in the real game you would right click to put a flag there. But this simulator can’t do right clicks.)

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We are Going to Fast Forward Now

See if you can find the next safe square based upon the logic we have been using. Look for a square by the square we just flagged that logic tells us is safe.

Once you click the right square, this simulator will do some more moves for you. (The real game won’t!)

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Watch As We Make Some Moves

Watch these moves being made. Think about why these moves are all safe.

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Faced With the Number 2

So far we have mostly dealt with using squares that have a 1 in them to figure things out. But squares that contain a 2 can also be useful. Remember that the number tells you how many bombs surround it. Try to figure out from the square the magnifying glass is on, which other square has a bomb? Then click where you think the bomb is.

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You Flagged the Bomb

Now lets go back to using the number 1 as our clue. Click the next safe square based upon the square that has a 1.

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You Are Doing Good

Try another one that might be safe based upon the one you just clicked.

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Keep Going

You are doing good. Why don’t you click on the next one that is safe based upon the square with a 1.

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Many Options

At this point, there are many options for continuing. We could go back to using the squares with the number 1 in them, or we could find safe squares based upon those that have a 2. Or we could challenge ourselves…

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Challenge: Using Advanced Logic

By looking just at the three squares that have a 2 in them, with some advanced logic, you can deduce which unknown square has a bomb.If you want a challenge, try to figure out which one needs to be flagged as a bomb. This is fairly advanced, so if you want to just have us do it for you, click the button below:

Go Back Skip the Advanced Logic, Just Flag the Bomb for Me!

Here is the Bomb

Ok, now you have learned most of the basic logic that is needed to win a beginning level game. Sometimes there is even more advanced logic that is needed when playing on intermediate or expert mode. But for now you have done enough, and we will do some more moves for you, so sit back and relax…

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Watch and Think

Keep clicking the forward button below to see each move.While watching the moves, make sure you understand why each move is being made.

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Watch and Think

Keep clicking the forward button below to see each move.While watching the moves, make sure you understand why each move is being made.

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Watch and Think

Keep clicking the forward button below to see each move.While watching the moves, make sure you understand why each move is being made.

Go Back Go Forward

Watch and Think

Keep clicking the forward button below to see each move.While watching the moves, make sure you understand why each move is being made.

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Watch and Think

Keep clicking the forward button below to see each move.While watching the moves, make sure you understand why each move is being made.

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Watch and Think

Keep clicking the forward button below to see each move.While watching the moves, make sure you understand why each move is being made.

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Your Turn

One of the two boxes at the bottom is safe, and the other is a bomb.

You must find the one that is safe. Click on it. If you click the wrong one. You will need to restart this simulator.

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Good Job

You clicked on the right one. Since you did such a good job, we went ahead and flagged the bomb for you.

We’ll let you relax and watch for a little bit longer, as we do some more moves.

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Watch and Think

We will play through a few more moves for you. But don’t worry, you will need to make the final move.

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One Last Move

You are really close to winning. All you need to do is click on the safe square.

But be careful, if you click the wrong square, you will lose, and need to start the simulator over again!

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You did a great job, now you can either: try a real gameor redo the simulatororquit the simulatororgo to the wikiHow tutorial

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You Won!!

Playing a Real Game

• Click the Smiling Face with sun glasses to Start a Real Game of Minesweeper

• It will appear on the left side. • If you can no longer see the

game, click on Minesweeper on your task bar

• Click the smiling face to restart the simulator.

• Click the sad face to leave.

Sorry, You Blew Up(But You Can Try Again!)

Click on the face above to restart the simulator

Credits and LicensingThis minesweeper simulator is a creation of Jacob J. Walker for Twin Rivers Adult School and an assignment for NSU EDU 612 (Thinking for Results: Applying the Science of Student Achievement) in collaboration with the Effective Education Project. All content by Jacob Walker is released under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License. All other content licensed as listed here.Microsoft Windows Minesweeper Screen Shots and Icons used under the Fair Use clause of U.S. Copyright Law, with an attempt to adhere to Microsoft’s Copyright Rules. Microsoft does not endorse the use of their pictures and logos here, and all logos representing their products are their trademarks. Gender neutral singular pronouns such as “them”, “they”, etc are used purposely with long standing prior-art .

Quit Restart Simulator