Creative Matchstick Puzzles Innovative Solutions

By Atanu Chaudhuri

To give you an idea on how the humble little matchsticks can be used in making puzzles that can give you lots of creative fun, we have handpicked 50 matchstick puzzles in this book.
Each chapter starts with the description of the puzzle with a recommended time to solve. Our suggestion: don't look at the recommended time. Just solve the puzzle. After all, it is no exam!
After the puzzle description, we have solved the puzzle using analytical methods. Each chapter is like that. In fact, the puzzle solutions make up more than 90% of the book.
The solutions highlight how systematic analysis, reasoning, and innovative methods can solve a puzzle in a structured manner without any guesswork. The important concepts and techniques are explained in brief in the last chapter. You may refer to it time to time to get the feel of how a tricky puzzle may be solved.
You may use the book as a collection of interesting puzzles to indulge in a creative fun-filled time.
If you go through the solutions as well, you will discover a whole new world of systematic and innovative thinking. It will change the way you think!
The puzzles can be enjoyed by the young and the old alike.
Happy puzzling!

• Language: English
• Publisher: Atanu Chaudhuri
• Release date: Sep 5, 2023
• ISBN: 9798223045496

Book preview

Part 1

Puzzles & Solutions

Chapter 1

First Move 3 matches and make 2 squares puzzle

In puzzle figure, move 3 matches to make 2 squares.

How many unique solutions can you find?

move-3-sticks-to-make-2-squares-1-matchstick-puzzle

Time limit: 5 minutes.

Unique solution: If you rotate the solution figure, it will remain unique under any situation.

Give it a try. It will be fun.

Comment

The puzzle differs from the matchstick puzzles we see usually. There is no complete square or triangle in the puzzle figure.

It looks as if the figure is incomplete.

How to solve it?

You may select any 3 sticks you like and try to place the sticks to make 2 squares. That would be the trial and error method. Usually, that takes more time.

Instead, spend a little time to analyze the puzzle figure. Think about how the solution figure would look like. And then decide on your stick moves. You would solve the puzzle quick this way.

Solution to Move 3 matches to make 2 squares matchstick puzzle 1: By Structural analysis Identify which sticks to move and where to move

First stage: Analysis of number of sticks used

Take the first step. Count the number of sticks. It is 10.

Make the first conclusion.

Conclusion 1: To make 2 squares by these 10 sticks, the 2 squares must be of UNEQUAL SIZE.

Reason for unequal size: To make two squares MAXIMUM number of sticks required is 8 when the two squares do not have any common side. Puzzle figure has 10 sticks, more than the maximum.

That’s fine. Easily accepted.

Question: But what would be the size of the two unequal squares in the solution figure?

With a little thought, make the second conclusion,

Conclusion 2: The two squares must be: One large square of 2 stick sides and one small square of 1 stick sides.

Reason:

A large square with 3 stick sides requires 12 sticks for its 4 sides. This is more than number sticks in puzzle figure.

As two squares with 2 stick sides is not possible, one large square MUST BE of 2 STICK SIDES and one small square of 1 stick sides.

Okay. But how would the two squares be placed in the solution figure?

Analyze the number of sticks available and number of sticks required to make two such squares.

Also, use the concept of COMMON STICK. Each common stick between two squares reduces the number of sticks required to make the squares by 1.

Conclusion is easy.

Conclusion 3: One square of 2 stick sides requires 8 sticks. 2 more sticks are left from 10 available. A single small square requires 4 sticks making total sticks required 12. So 2 sticks must be common between the two squares.

Question: What can be the location of the small square in relation to the large square?

Conclusion 4: The small square cannot be located outside the large square as it would have then only 1 stick common with the large square. Need is for 2 common sticks. isn’t it?

Conclusion 5: That means—the 3 STICKS TO MOVE must be the three sticks of the small square in the puzzle figure, leaving its right vertical stick.

This settles the first issue—which sticks to move.

The following figure shows the results of reasoning achieved till now. You are now sure that the check-marked sticks are the sticks you have to move.

move-3-sticks-to-make-2-squares-1-matchstick-puzzle-sticks-to-move

Nothing random or extraordinary you have done. It has all been common sense reasonable questions and clear conclusions.

Final stage of Solution to Move 3 matches to make 2 squares matchstick puzzle 1: Where to place the 3 sticks?

The large incomplete square has two gaps to close on its right side. Isn’t it?

So move two of the check-marked sticks to close the two gaps. The large square is now complete and one stick left to move.

Look at the figure you have made by the two stick moves. What do you see?

Conclusion 6: Using the stick left, a small square can be completed in TWO WAYS. At top right or bottom right.

Both are solutions to the puzzle.

Following figure shows the solutions.

move-3-sticks-to-make-2-squares-1-matchstick-solutions

So you have found not one, but two solutions to the puzzle step by step.

But the question arises—are these two solutions rotationally unique?

Second part of the solution to Move 3 matches to make 2 squares matchstick puzzle 1: How many rotationally unique solutions?

Just rotate the first solution figure by 90 degrees clockwise and you will get the second solution. These two are equivalent.

Rotationally UNIQUE SOLUTION IS ONLY 1.

Takeaway

The puzzle is easy to solve. But it feels good to know exactly what to do and why to do it. All through the steps of solving the puzzle. Isn’t it?

This is innovative problem solving by analytical reasoning step by step.

Concepts used: Common sense reasoning and matchstick structure concept of common sticks.

End Note

If you create your own matchstick puzzle and solve it exhaustively, using all methods you know and can create, it will be a richly rewarding experience and an interesting pastime.

Chapter 2

Second Move 3 sticks and make 2 squares matchstick puzzle

The Matchstick Puzzle

Part I: In the puzzle figure, move 3 matches to make 2 squares.

move-3-sticks-to-make-2-squares-2-matchstick-puzzle

Part II: How many unique solutions can you find? A unique solution means—if you rotate the solution figure, it will remain unique. And you have to find ALL such unique solutions.

Total recommended time: 5 minutes.

Enjoy!

Comments

The matchstick puzzle figure is not made up of usually encountered complete regular geometric shapes of squares or triangles. It does not have any such single closed shape. And it comprises a fairly large number of 15 sticks.

How should you proceed?

You can go ahead by using trial and error, but usually that takes more time. Instead, if you do a bit of analysis, you can reach at least one solution quickly. And that’ll solve the first part of the puzzle.

Solution to 2nd Move 3 matches to make 2 squares puzzle: Structural analysis and reasoning: Identifying which sticks to move

First step of solving any matchstick puzzle is to count number of sticks—it is 15.

Obviously, to make 2 squares out of these 15 sticks,

Conclusion 1: The 2 squares must be of unequal size—one large square with 3 stick side length and one small square of 1 stick side length.

Why not 4-stick side larger square?

Reason: Four-stick long sides of a square would require 16 matchsticks. Even if you create the 1-stick side smaller square attached in a corner of the larger square, the number of common sides will be 2, and the total number of sticks required would be 16+4−2=18, more than what you have.

And if you attach the smaller square anywhere else inside the larger square, the number of common sides will be only 1, and the total number of sticks used would further increase by 1 to 19.

Think over: Why you cannot use 3-stick side larger square and 2-stick side smaller square. Use similar logic.

How can you use 15 sticks to form two squares?

Number of sticks required to make two such independent squares, one 3 stick side and the other 1 stick side, would be, 12+4=16.

As you have 15 sticks,

Conclusion 2: There must be 1 stick common between the two squares reducing the number of sticks needed from 16 to 15.

The third conclusion is easy to make,

Conclusion 3: You have to close the gap of the larger square, AND form the 1-stick side smaller square attached to the middle stick of any side of the large square.

If you form the small square at any corner of the large square, there would be 2 common sticks, not 1. Sticks used would then be 14, not 15.

2nd move 3 matches to make 2 squares matchstick puzzle: Which sticks to move?

Candidates obviously are the four sticks inside the larger square.

It seems, you may keep stick 1 undisturbed, but sticks 2, 3 and 4 you should move as these are well inside the larger square. These three will be isolated and left hanging if stick 1 closes the gap to complete the larger square.

The following figure shows the four candidate sticks numbered.

move-3-sticks-to-make-2-squares-2-matchstick-puzzle-sticks-to-move

Which 3 of the four sticks are to be moved?

Final stage of solution to 2nd move 3 matches to make 2 squares matchstick puzzle: Convenient position of stick 1 helps quick solution

You have already concluded that the new smaller square must be formed attached to the middle stick of a side of the larger square (so that the number of common side is 1, not 2).

This is what we call as a BINDING CONDITION that cannot be violated.

You have stick 1 already waiting for the other two sides of the smaller square to be formed. So it is convenient not to be moved.

Solution is now clear,

Move any of the 3 sticks numbered 2, 3 and 4 to close the gap of the larger square, and form the smaller square with the rest two free sticks and existing stick number 1.

Following figure shows the solution.

move-3-sticks-to-make-2-squares-2-matchstick-puzzle-solution

2nd move 3 matches to make 2 squares matchstick puzzle: How many unique solutions?

For a moment forget the convenience of keeping stick 1 unmoved. Open your mind to all possibilities without any bias.

If instead of stick 1, you keep stick 2 fixed can you not make another similar solution shape?

Why, yes. You can.

Close the gap of the large square by stick 1 and complete the two other sides of small square by moving stick 3 and stick 4 with stick 2 already waiting as an existing side.

The small square is formed in this case on the left vertical side of the large square.

This will be the second solution.

Well, well, you can also form two other solution shapes by keeping fixed stick 3 and stick 4, respectively.

With stick 3 fixed, the small square is formed on the bottom horizontal side and with stick 4 fixed, the small square is formed on the right vertical side of the larger square.

There can then be four solutions that look different.

If you don’t rotate, you will have 4 unique solutions, but if you rotate any of the solution shapes it’ll be same as the other three.

Rotationally unique solution is only 1.

You have taken care of all possibilities! Exhaustively.

End Note

If you form your own matchstick puzzle and solve it exhaustively using all methods you know and can create, it will be a richly rewarding experience and interesting pastime.

Chapter 3

Move 3 matches to make 3 squares Tic Tac Toe matchstick puzzle

Move 3 matches to make 3 squares from the Tic Tac Toe matchstick figure.

Tic-Tac-Toe-move-3-matches-to-make-3-squares-puzzle

How many unique solutions can you find?

Recommended time to solve: 5 minutes.

Give it a try. It will surely be fun.

Hint: Use your analytical reasoning instead of random trial and error.

We’ll solve the puzzle step by step by analyzing the puzzle structure and making conclusions based on common stick constraint and a series of questions, analysis and answers.

Solution to Move 3 matches to make 3 squares Tic Tac Toe Matchstick puzzle: Structural analysis, Common stick analysis, Chain of reasoning by Question analysis answer

The following is the Tic Tac Toe matchstick puzzle figure with each stick numbered uniquely. This will help us explain.

Tic-Tac-Toe-move-3-matches-to-make-3-squares-sticks-numbered

First step in solving any matchstick puzzle is to count number of sticks in the puzzle figure. It is exactly 12.

Question 1: How many matchsticks do you require making 1 square?

Answer: It is 4.

Question 2: How many sticks would you need to make 3 INDEPENDENT squares.

Answer: 2: To make 3 independent squares you need exactly 12 matchsticks that you already have.

As you know that if there were a single stick common between two squares need for sticks would have reduced by 1 to 11, you can make your first conclusion. This is a key conclusion or key pattern identification based on the common stick concept.

Conclusion 1: The three squares in the solution figure won’t have any common stick between any two of them.

Note: This is what we call key pattern identification and precise requirement specification for the final solution. Subsequent analysis and decisions will follow from this result.

Chain of reasoning based on common stick constraint and Identification of sticks to move

Look at the puzzle figure and take stock.

Observation: There are four nearly complete squares in the tic-tac-toe. Each has three sides already in place (three times four makes up the 12 sticks). Only 1 stick is required to close the fourth side and complete a square in each.

These are,

I: Sticks 1, 5, 3.

II: Sticks 4, 8, 12.

III: Sticks 11, 7, 9.

IV: Sticks 10, 6, 2.

Conclusion 2: Some of these four one side only open nearly complete squares must be completed to make the final solution figure. This is an obvious conclusion.

Now ask yourself the question,

Question 3: What would be the situation if any of these nearly complete squares is completed?

Just assume, the square with sides 10, 6, 2 is completed by moving stick 1. Any problem you observe?

Answer 3: Yes there will be a serious problem.

It will create a common stick 6 with the existing central square made up of sticks 5, 6, 7, 8.

An example is shown for making the consequence clear. This is not trial and error. This is the well-used and highly valuable management technique of Consequence analysis.

Tic-Tac-Toe-move-3-matches-to-make-3-squares-puzzle-invalid-square

That’s why you have to make the third important conclusion,

Conclusion 3: To make the solution you want, the central square MUST be destroyed by selecting one or more than one stick among 5, 6, 7, 8 for moving.

As all the four nearly complete squares are STRUCTURALLY EQUIVALENT, you may choose any of the four.

Action 1: So you choose stick 5 with full confidence that this must give you a solution. And move it straightaway to complete one of three remaining nearly complete squares, say square with three sides 11, 7, 9.

The result of the action is shown below.

Tic-Tac-Toe-move-3-matches-to-make-3-squares-puzzle-intermediate-solution

Well, well, well. You have got the solution in your pocket with this single confident action.

The two sticks 1 and 3 are hanging, ready to be moved to complete the other two squares, the square with three sides 10, 6, 2 and the square with three sides 4, 8, and 12.

Following results from these actions. We have kept the original sticks that we have moved, but made them faded to give you a very clear idea on how you have created the solution figure from the starting figure.

Tic-Tac-Toe-move-3-matches-to-make-3-squares-puzzle-solution

Consider that you could have selected any of the other three one-side-open-three-stick components to form three perfect squares. But the result would have been the same if you would just rotate the figures suitably.

So we conclude,

These three other solutions