## Move 3 matches to make 2 squares matchstick puzzle 1

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

How many unique solutions can you find?

**Time limit:** 5 minutes.

**Unique solution: **If you rotate the solution figure in any way, it will still remain unique.

Give it a try. It will be fun.

### Comment

The puzzle is different 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 and conclusions

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 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 with respect 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 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.

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.

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

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

#### Second part of 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 **systematic problem solving** by analytical reasoning step by step.

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

### 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 as well as **interesting pastime.**

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