## Create 7 squares by moving 5 matchsticks

In the matchstick puzzle figure, move 5 matchsticks to create 7 squares. No matchstick should be left hanging without being part of a square.

**Recommended time to solve** is 10 minutes.

Give it a try before you go through the solution.

### Solution to the matchstick puzzle move 5 matchsticks to create 7 squares: Matchstick count and common side analysis

Total number of matches is 18 whereas 28 matches would be required to create 7 independent squares. First conclusion formed is then,

Conclusion 1:There should be 10 common matches in the final solution of 7 squares.

But that is a lot of common matches. The final solution figure must be very compact.

Let us examine the most compact 6 squares and 7 squares figure, as shown.

The square A is attached as an extension to the most compact six squares figure. In this arrangement you have 20 matchsticks, two more than what we have.

Conclusion 2:The figure being the most compact 7 squares figure, the only possibility to have 7 squares with 18 matchsticks is - the matchstick squares must be of different sizes.

With this awareness, the count of squares increases in the figure to 9. Extra are the two numbers of 2-stick side squares.

A candidate solution will then be formed by removing the two marked sticks and moving up the three external sides of square A by one square. This eliminates one small square and one 2-stick side square, making the number of squares 7 as needed.

The candidate solution is shown.

But can we form this candidate solution figure by moving 5 matches of the puzzle figure? Yes, we can, and the candidate solution is a real solution, as shown.

Is this the only solution possible? Think for a moment.

The rightmost single square is located vertically at the middle of the structure. **It can easily be at the top right to form the second solution.**

As the five squares component of the most compact six squares part cannot be disturbed compactness and structural point of view, these are the only two possible solutions.

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