Move 4 matchsticks to make 6 squares from the 5 square matchstick puzzle figure. Time to solve 10 minutes. Give it a try. It's a not too hard fun puzzle.

### The matchstick puzzle

Move 4 matchsticks to make 6 squares from the 5 square matchstick puzzle figure.

All matches in the solution figure must be a side of a square.

No 6 square matchstick figure should be formed in an intermediate stage before completing the movement of all four matchsticks.

**Time to solve the puzzle:** 10 minutes.

This is a not too hard fun to solve puzzle. First, give it a good try before looking into the detailed step by step solution.

### Solution to move 4 matches to make 6 squares matchstick puzzle: Analysis

The matchstick square puzzle figure is shown again for convenience.

The matchstick puzzle figure comprises 5 independent matchstick squares made up of 20 matchsticks with no single matchstick common between any two squares. On the other hand, we have to form 6 squares from the same 20 matches.

To make 6 independent squares, we need 24 matches. So when 6 squares are made from 20 matches, 4 matches must be common between squares. This reduces the maximum match requirement from 24 to 20.

Conclusion 1:The solution matchstick figure of 6 squares must have 4 common matches between squares.

#### An example of an invalid solution figure with 6 squares

A 6 square figure made by the 20 matches by moving just 2 matches from the 5 square puzzle figure is shown.

This is an invalid solution, as we have to move 4 matches to form the 6 square solution figure and not just 2 matches.

What do we learn from the invalid figure? First, the solution cannot be such **a pair of three adjacent squares** and second, the **solution can’t be achieved by moving matchsticks from the central square.**

The clues show simply that,

Conclusion 2:The solution would be formed by moving matches from any of the four corner squares, as all four are equivalent to each other.

#### Analysis of the number of squares to form, number of squares to be destroyed and sticks that can be moved

If we move any single matchstick from a **corner square**, we will destroy **one square and create three hanging sticks.** We have to move at least one more of the three hanging matches.

This way, if we move two of the four matches from a corner square, the only option to use the matches would be to close two of the four existing one side open unfinished squares. The new formation is shown,

Again, moving just 2 sticks 6 square formation is created. This is the second invalid solution and we can conclude that,

Conclusion 3:We cannot move 2 corner matchsticks from a corner square and create 1 square by each of the two matches moved.

It follows,

Conclusion 4:We willmove 1 match from the selected corner square and close a suitable incomplete square.

That will make a new square and will compensate the square destroyed.

Conclusion 5:And with therest three of the four hanging sticksof the square destroyedwe will form a second square using a suitable existing side as the base.

The final solution shown.

The matchsticks selected for movement are faded out and marked by a single red stroke, while the final place to which the matches are moved are marked by double red strokes.

In addition, arrows show the matchstick movements.

#### End note

As we have formed the only feasible scheme to form a solution, you can try to form additional solution figures applying the scheme.

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