In the puzzle figure, move 3 matches to make 7 squares. You have 5 minutes to solve the puzzle. And know how to solve easily from the solution.

### Matchstick puzzle Move 3 matches to make 7 squares

In the following puzzle figure, move 3 matches to make 7 squares from 5 squares. All squares must be of equal size and each matchstick must be a side of a square.

**Time to solve:** 5 minutes.

First give it a try and then go through the solution to know how the puzzle can be solved easily applying step by step reasoning.

### Solution to matchstick puzzle move 3 matches to make 7 squares: Common matchstick analysis

First task in solving a matchstick puzzle is to count the number of matchsticks. The puzzle figure comprises 20 matchsticks. It is shown again for convenience.

7 squares are to be made from 5 squares.

To make 7 independent squares, how many matchsticks would be needed? It would be 28 matchsticks needed, 8 more than what we have.

How will it be possible?

This is where the common matchstick concept comes in to provide the suitable solution. By this **common matchstick concept,**

Every matchstick common between the two closed shapes reduces the number of matchsticks needed to form the two closed shapes independently by ONE.

Use this concept to draw the first conclusion.

Conclusion 1:As 20 matches are to be used for making 7 squares that need 28 matches to make them independent of each other, there must be 8 common matchsticks in the final figure.

Let us forget for a moment how to form the solution from the starting puzzle figure.

Let us just try to imagine how the 7 squares can be formed using 20 matches only.

We’ll proceed part by part, **first taking up the most compact form of 4 squares.** This is the use of the **problem breakdown technique.**

We know from experience that the most compact formation of 4 squares is where the figure has four common matchsticks. This is the maximum number of common matches possible between 4 squares and is shown.

And in a most compact formation of 3 squares, the maximum number of common matches is 2. It requires then 12 - 2 = 10 matches whereas the 4 square figure above needs 16 - 4 = 12 matches.

These two most compact figures shown below together require 10 + 12 = 22 matches, 2 more than what we have.

Slide left the 3 square figure to merge with the 4 square figure forming a 7 square figure. Two more common sides between the two will reduce the need of number of matches to 20 exactly the number we have.

The 7 squares made up of 20 matches shown below. This is our target solution figure.

#### Solution to move 3 matches to make 7 squares matchstick puzzle: Forming the target solution figure from the puzzle figure

Technique to identify the matches to move for making the target solution figure from the puzzle figure is to **mentally superimpose one onto the other.** This critical action** identifies the components common between the two.**

With this technique, it is easy to identify the common squares between the two. This is shown below.

Four squares A, B, C and D are common. Rest three matches are the three moved ones marked red, whereas the match marked green would be the base of the 5th square that would have to be destroyed in forming the 7 squares.

The final solution is shown below with the matches moved marked by arrows and faded out in their original positions.

#### End note

A matchstick puzzle may be solved in different ways, but this is how this puzzle is solved step by easy step, using the basic properties of the matchstick shapes and reasoning.

There is no substitute for **systematic problem solving** when assured and quick solution is the call of the day.

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