## The puzzle: Move 3 sticks in the figure and form 2 squares

This is the 14th matchstick puzzle with solution. You have to **move 3 matchsticks in the figure shown and make 2 squares.**

The second part of the question is: **how many unique solutions can you find? **A unique solution means—if you rotate the solution figure in any way, it will still remain unique. And you have to find ALL such unique solutions.

*To solve the two parts of the puzzle problem, recommended time is 10 minutes.*

One request before we proceed to solve the puzzle—please try to solve the puzzle before you look through the solution.

### Soluton: Second puzzle of Move 3 sticks to make 2 squares

Let us show you the figure again.

The matchstick puzzle figure is not made up of complete regular geometric shapes of squares or triangles. The figure is incomplete.

How should we 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. That's the first part of the puzzle.

#### Structural analysis and reasoning—Identifying which 3 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, 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. **This is the first conclusion.**

Number of sticks required to make two such independent squares would be, $12+4=16$. As we have 15 sticks, there must be 1 stick common between the two squares reducing the number of sticks needed from 16 to 15. **This is the second conclusion.**

The **third conclusion** is easy to make—you have to close the gap of the larger square, AND form the 1 stick side length smaller square **attached to the middle stick of a side of the large square.** If you form the smaller square at any corner of the large square, there would be 2 common sticks, not 1.

Which sticks to move? Candidates obviously are the four sticks inside the larger square.

The following figure shows the four candidate sticks numbered.

Which of the four sticks are to be moved?

#### Final stage of solution: Movement restrictions on stick 1 forces 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 number of common side is 1, not 2).** You have stick 1 already waiting for the other two sides of the smaller square to be formed. So it cannot be moved.

Solution is just one step more.

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 already existing stick number 1.

Following figure shows the solution.

**How many unique solutions?**

This is the **only ONE solution** because, **1 side of the smaller square, stick numbered 1, remains unmoved.** You cannot form the smaller square in any other way.

#### 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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