## Move 3 matches to make 4 squares

Move 3 matches to make 4 squares from 5 squares puzzle figure. This is the 4th 5 squares matchstick puzzle of this type. You have to solve it in 10 minutes.

### The 5 squares matchstick puzzle

You have to move 3 matches to make 4 squares in the 5 square matchstick puzzle figure with no stick left hanging.

In how many ways can you do it?

*Total Recommended time is 10 minutes.*

Before this we have solved three more 5 square to 4 square puzzles with different starting configurations.

Even if you have gone through any of those, this puzzle should give you new food for thought. Just give it a try.

### Solution to the 5 squares matchstick puzzle: Move 3 matches to make 4 squares from 5 squares

We’ll take up a completely analytical approach to arrive at conclusions based on basic matchstick puzzle concepts and deductive reasoning.

#### Analysis of the structure and knowing precisely what you have to do

**At the first step,** you need to always ** count total number of sticks. It is 16 for this configuration.** These sticks form 5 squares.

How many sticks are required to form a SINGLE square? It is 4. *So to form 5 squares 20 sticks would have been used*—4 more than the 16 sticks we have.

*How could 5 squares have been formed even with a number of sticks 4 less than the number needed to form 5 squares?*

This is where the *key concept in matchstick puzzle solving* comes in—the **concept of sticks common between two adjacent unit shapes.**

In our problem, the **unit shape is a square.** In another puzzle, the figure could comprise equilateral triangles. There can be many variations. But the fact remains,

Each common stick between two unit shapes reduces the number of sticks required to form a figure with the two shapes independent from each other—by ONE.

The 4 common sticks in the puzzle figure reduced the requirement of 20 sticks to form 5 independent squares to 20−4=16 sticks.

Now look at our 5 square figure again—this time we have labeled the squares A, B, C, D and E, so that we can refer to a specific square.

You have exactly 16 sticks, the maximum number required to form 4 independent squares. 4 common sticks reduced the maximum requirement for 5 squares from 20 to 16. Our job is then clearly to,

Eliminate all 4 common sticks and form 4 independent squares by moving just 3 sticks.

**In this second step**, *you have precisely and clearly understood what you have to do to solve the puzzle.*

#### Solution by analyzing the puzzle figure

The 5 square problem figure is now shown below with 4 common sticks check-marked and numbered 1 to 4. Three more sticks are also numbered.

The central square C has each of its 4 sides as a common stick. In the solution, there has to be NO common stick. The **first certain conclusion** you can reach is then,

In the solution,

you cannot have this square C—you must destroy it in moving 3 sticks—alsodestroying 2 squares and creating 1 new square.

This is the **key pattern and must-do action identification.**

You may wonder—why destroy 2 squares? The answer is simple—you have to destroy square C by moving any of its side sticks. Say you move the right **vertical stick 4** in square C. What happens?

Not only does square C gets destroyed, but square D also is destroyed. It is natural.

As each side stick of square C is a stick common to two squares, as soon as you move one of these 4 common sticks two squares are gone.

Right?

So by moving the right vertical side stick 4 of square C you have made 3 sticks of square D—sticks numbered 5, 6 and 7 free to move.

Out of these 3 free sticks, ** you can move only two** and

*using these two with the first one moved*you have to

*form the new fourth square.*

This is the **second certain conclusion.**

*Which two would you move now and which one would you keep untouched?*

*You have only one choice.*

You have to keep the right vertical stick of square D—stick 6 untouched.

This is the **third certain conclusion.**

**Your task:** *Check the truth of this third conclusion and find the reasons behind it.*

There is your solution below.

The red, blue and green colored sticks of now gone square D are moved to form the NEW fourth square with its fourth side as stick 6 untouched in its previous state.

Not difficult at all. Isn’t it?

Point is—the solution is not the most important thing—more important is how you reach the solution, the reasoning, conclusions and the actions.

Okay, this is one solution of the puzzle.

Now you have to find the answer to the second part of the puzzle—**is there any more solution(s).**

### Can we form 4 squares from the figure of 5 squares in any other UNIQUE way by moving 3 sticks?

As you know various aspects of the puzzle figure well now, you would immediately be able to identify three more possible solutions in which earlier numbered sticks 1, 2 or 3 is moved first. The NEW squares would have to be formed on the single untouched stick of square E, B and A respectively.

A possible solution in which the new 4th square is formed on the vertical untouched side of earlier square B is shown below. In this configuration, squares A, D and E are not touched.

Is it a new solution? Give it a thought.

If you ** flip the first solution figure horizontally by 180 degrees you’ll get this figure.** This solution is not then a rotationally UNIQUE solution.

To get the other two possible solution figures, you have to rotate the first solution by 90 degrees, clockwise and anti-clockwise.

There is only **ONE UNIQUE solution to the puzzle.**

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