Matchstick puzzle, Turn around the fish by 3 moves

Submitted by Atanu Chaudhuri on Thu, 18/07/2019 - 21:00

Matchstick puzzle move 3 matchsticks to make the fish swim left

Matchstick puzzle - Move 3 matchsticks to make the fish swim left

The matchstick puzzle fish swims to the right. Move 3 matchsticks to make it swim left. It's a fun matchstick puzzle that you must try to solve.

Recommended time to solve: 10 minutes.

matchstick fish swimming towards right

The matchstick puzzle seems easy, though it is not. That's why it is one of the most popular among all matchstick puzzles.

Give it an honest try. You will enjoy solving the problem.

If you don't find the solution or feel curious about how we have solved the puzzle, then do go through the solutions.

We have approached the problem using analysis and reasoning. Results of initial problem analysis and reasons behind each action made as clear as possible.

Major part of the solution is observation and analysis moving on to the final solution.

And we are sure you would find our experience valuable. This really is an interesting little problem.

Solution to Matchstick puzzle - Move 3 matchsticks to make the fish swim left

The following is the turned around fish. It is now swimming exactly opposite towards left. This is the final solution figure. We have to find how to make this from the matchstick puzzle fish in 3 matchstick moves.

matchstick fish swimming towards left

It is natural to form the solution figure first and then try to see how to reach the solution.

This is initial quick trial.

We took a minute to form this turned around fish in 4 stick moves. And then went back to the original configuration, retaining the idea of final image.

Keeping the final matchstick fish in front of our eyes was distracting.

It is easier to analyze the initial matchstick puzzle figure and identify sticks that we must not move. Then it would be easy to identify the sticks to move to make the solution figure.

This is stick move analysis, one of the main approaches to solve a matchstick puzzle.

Solving a matchstick puzzle always needs structural analysis of the puzzle figure in some way.

Structural analysis of matchstick puzzle fish - chain of reasoning and conclusions

Following is the rightwards swimming matchstick puzzle fish with each of its stick members numbered uniquely.

matchstick fish swimming towards right numbered

Analysis:

Other than the combined HEAD and BODY, the matchstick fish doesn't have any closed shape.

Details of sticks of its components are,

Matchsticks 1 and 2 make up the HEAD and together with 3 and 4 make up the HEAD and the BODY.

Matchsticks 7 and 8 make the TAIL-FINS and matchsticks 5 and 6 make the two BODY-FINS.

Observe that the ONLY CLOSED COMPONENT is the HEAD and the BODY made up of four sticks.

We could have kept this component untouched to easily form the tail-fins and body-fins by moving the four other sticks. But that would be moving 4 sticks. Wrong.

Too easy and no fun. Not this puzzle.

You have no other option than to,

Form another HEAD and BODY.

That is the most important component without any doubt. All other components hang on to it.

What does it mean to form another head and body? Answer is simple,

You have to form a NEW closed SQUARE.

This is the first important conclusion. It will help to identify sticks to move leading you to the solution.

As the number of stick moves allowed is low, you must keep an eye to move minimum number of sticks.

It follows then,

You have to form a new closed square by minimum number of stick moves.

This is the key conclusion made by step by step analysis and reasoning on the puzzle structure. Once you are confident that it is true, you can visualize the solution.

Analysis:

It is always possible in this structure to form a new closed square by moving 2 sticks, but that would be too many.

In that case, in one remaining stick move, you have to form the new tail-fins and body-fins. An impossible task.

So it follows,

You have to form the new square in one stick move. That is possible only when the other three sides of the square are already in place.

The numbered fish is shown with important sticks colored.

matchstick fish swimming towards right numbered colored 1

Stick groups 4, 6 and 8 as well as 5, 3 and 7 each form an incomplete square with three existing sides.

As these two possibilities are equivalent because of symmetric position, let's select the three sticks 4, 6 and 8 for making the HEAD of the turned around fish.

Its single open side is to be closed by 1 stick move.

Question is—which stick should we select to close it?

There may be more than one possibility and we will take a safe path of reasoning,

As the old head has to be destroyed (we are forming a new head pointing in opposite direction, right?), one of the two sticks 1 and 2 must be moved. Which one?

In this advanced stage it is easy to identify stick 2 to play the role of a body fin in the new figure. So we won't move it, That leaves the only choice of stick 1 to move.

This is chained reasoning.

The stick 1 moved to its new position forming the new head and body is shown in the solution figure below.

The rest of the two sticks to be moved are also colored for convenience of understanding.

matchstick fish swimming towards right numbered colored 2

At this stage, it is easy to identify stick 3 as one of the new body fins already in place, and so we won't touch it.

The other two sticks, 5 and 7 are to be moved. The two are colored differently. One will form the second tail-fin and the other, the second body-fin.

There is no specific choice or sequence of movement.

Vital was the first stick movement.

The finished turned around fish is shown below.

matchstick fish swimming towards right turned left

The original positions of the three sticks moved are shown faded out to convey a clear idea about which sticks are moved to which positions.

End note

We have analyzed the problem step by step. Questions are raised and answers formed after analysis. Possibilities narrowed down to the solution.

This is systematic approach to problem solving.

It depends on identification of key patterns, creation of effective methods and deductive reasoning. As a result, solution reached without confusion and in a short time.

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.