Matchstick puzzle, Move 3 sticks in tic-tac-toe figure to form 3 perfect squares

Submitted by Atanu Chaudhuri on Fri, 19/07/2019 - 16:50

make 3 perfect squares by 3 stick moves

The puzzle: Move 3 sticks and form 3 perfect squares

This is the fifth matchstick puzzle with solution.

The following is the tic-tac-toe figure made up of matchsticks. You have to move 3 sticks to form 3 perfect squares. You have 10 minutes recommended time to solve the puzzle.

move 3 to make 3 perfect squares

This puzzle is interesting but relatively easy. So we recommend 10 minutes for solving the puzzle. We assure you that you will enjoy solving the problem.

By chance if you can't find the solution in time or feel curious about how we have solved the puzzle and what are the reasons behind our selecting the three sticks one after the other, then you should go ahead and go through the solutions.

As always we have approached the problem analytically, and have tried to explain our initial problem analysis results and the reasons behind our actions as clearly as possible.

Solution to the puzzle: Move 3 sticks in tic-tac-toe figure and form 3 perfect squares

The following is tic-tac-toe figure with each stick numbered uniquely so that we will be able to explain clearly our analysis and required actions.

move 3 to make 3 perfect squares numbered

First conclusion

Ultimate objective is to form 3 perfect squares and you have in total 12 sticks. In most of the matchstick puzzles involving triangles or squares, this is where we start. We try to form a clear idea about,

How many sticks will be common between two squares in the final figure.

As you know, each common stick will reduce the number of sticks required to form 3 perfect squares, that is, $3\times{4}=12$ by 1.

The certain conclusion is then,

As you have exactly 12 sticks, there will be no common stick between any two adjacent squares.

This is what we call key pattern identification as well as precise requirement specification for the final solution. Subsequent analysis and decisions will follow from this result.

Now we will start a chain of reasons.

First: There are four numbers of one side open nearly completed components of three sides already present. One is formed by sticks 1, 3 and 5 for example. Each of these components is a candidate for a perfect square by just 1 stick move.

Second: But you have to form 3 squares, not 4 and that too in 3 stick moves. So you must destroy one of these 4 components and use its sticks. You cannot keep any stick hanging, not as a part of a square.

Third: If you destroy one component of one-side-open-three-sticks out of four, three will be left and you have to form three squares from these 3 components by 1 stick move for each. You would need 3 sticks and you would get these 3 sticks from the three-stick component you have decided to destroy.

The following is the figure with three sticks identified for reuse shown as colored green.

move 3 to make 3 perfect squares numbered colored

Solution is now easy. Move stick 1 to close the open gap side between sticks 2 and 10, move stick 3 to close the open gap between sticks 4 and 12 and lastly move stick 5 to close the open gap between sticks 9 and 11. You have your 3 perfect squares.

Following is the result of these actions. We have kept the original sticks that we have moved, but made them faded to give you a very clear idea on how you have created the required figure from the starting figure.

3 perfect squares in 3 moves

Consider that you could have selected any of the other three one-side-open-three-stick components to form three perfect squares. But the result would have been same if you would just rotate the figures suitably. So we say, these three other solutions would be rotationally same with the solution you have created. That means, the solution is rotationally unique.

You may try for any other solution figure.

End note

We have approached the problem systematically and analytically, and not in any random way. This is what we call systematic approach to problem solving.

Generally, systematic approach to problem solving depends heavily on identification of key patterns, creation of effective methods and deductive reasoning to move towards the solution without any confusion as well as in minimum number of steps, if possible. That's why we call this as efficient problem solving.

Lastly, to solve matchstick puzzles you don't need to know maths or any other subject—you just have to identify key patterns and use your inherent analytical reasoning skills to home in to the solution with assurance and speed.