In the puzzle figure, move 3 matches to create ONLY 3 squares of different sizes. No stick should be kept hanging. Recommended time to solve 15 minutes.
Do try to solve before looking into the solution.
Solution to Move 3 matches to create 3 squares matchstick puzzle: Visualization of the final solution figure
We won’t think of how to move which sticks first. Instead, we would analyze to get an idea of the form of the solution figure.
What do we know of the solution figure?
It will be 3 squares. And ONLY three squares. With 18 sticks of the puzzle figure, how can only three squares be formed? It will be possible only if,
Conclusion 1: The squares are of three different sizes.
What can be the most possible three different sizes of the squares?
Conclusion 2: The most favorable three sizes of the squares must be 1-stick, 2-stick and 3-stick side squares.
To form a 4-stick long side square, too many sticks would be needed. So 1, 2 and 3 must be the side lengths of the three squares.
Now we will estimate the number of sticks to make three independent such squares as 4 + 8 + 12 = 24 that is 6 more than the 18 matchsticks of the puzzle figure. By common matchstick concept then, the solution figure will have 6 matchsticks common between the three squares.
With a good idea of the solution figure, we change our focus to concentrate on the puzzle figure now.
Can you predict how the three squares of side lengths 1, 2 and 3 sticks be formed from this puzzle figure?
Conclusion 3: It is obvious that the largest square would be the outermost incomplete 3-stick long side square of the puzzle figure. Three sticks are to be moved to complete this square.
At this point, the final solution becomes clear.
Final solution to Move 3 matches to form 3 squares matchstick puzzle
The following is the final solution.
The two smaller squares are outlined by coloring the boundary sticks. These are the squares A and B. The outermost largest square C is the third square of side length 3 sticks.
The three sticks in the second vertical are moved to complete the largest square, as shown by the arrows.
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