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Move 4 Matchsticks to make 6 Squares Puzzle

Move 4 Matchsticks to make 6 Squares Puzzle

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

The following figure has 5 squares made of matchsticks.

Move 4 Matchsticks to make 6 Squares Matchstick Puzzle graphic

Move four matchsticks to make 6 squares.

Conditions

  1. All matches in the solution figure must be a side of a square.
  2. No 6 square matchstick figure should form at an intermediate stage before completing 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 the move 4 matchsticks to make 6 squares matchstick puzzle: Analysis

The matchstick square puzzle figure is shown again for convenience.

Move 4 Matchsticks to make 6 Squares Puzzle Solution graphic

The matchstick puzzle figure consists of 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 thus reducing 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 reduction of maximum match requirement by a common matchstick is shown below.

Effect of one common stick between two squares

Forming an invalid solution figure with 6 squares

Following shows a 6 square figure made by the 20 matches by moving just 2 matches from the 5 square puzzle figure.

Move 4 Matchsticks to make 6 Squares Puzzle 1st invalid solution

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, solution can't be achieved by moving matchsticks from the central square.

The clues indicate 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.

Analyzing 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. Following shows the new formation,

Move 4 Matchsticks to make 6 Squares Puzzle 2nd invalid solution

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 matchsticks from a corner square and next 2 from s second corner square.

it follows,

Conclusion 4: We will move 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 the rest three of the four hanging sticks of the square destroyed we will form a second square using a suitable existing side as the base.

Following shows the final solution.

Move 4 Matchsticks to make 6 Squares Puzzle solution

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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