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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