## The matchstick puzzle: Move 3 matchsticks to rotate the fish to the left

A fish, formed by 8 matchsticks, is swimming towards the right. Move just 3 matchsticks to turn it around so that it swims now heading towards left.

**Recommended time** to solve: 10 minutes.

The puzzle is deceptively easy. Perhaps that is the reason why it is one of the most popular matchstick puzzles among all.

Give it an honest try. 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.

Major part of the solution will be observation and analysis that will quickly move onto the solution.

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

### Solution to the matchstick puzzle: Turn the swimming angel fish exactly around by moving just 3 sticks

The following is the turned around fish. It is now swimming exactly opposite and towards left. First impulse is always to form the solution first and try to see how you can reach the solution from the initial configuration.

True we have *formed this turned around fish in 4 stick moves in a minute* and then went back to the original configuration. We remembered the idea of the final configuration, but removed the exact configuration from our area of vision. We found it distracting.

It was much easier to quickly analyze the **initial fish structure**, decide *which sticks must be kept unmoved* and which sticks can be moved, and select the first, second and third stick to move.

Solving matchstick puzzles at the core, is structural analysis of the components of the puzzle figure.

Let us show you the initial figure of fish with each stick marked for ease of following the explanation.

#### Structural analysis of matchstick figure, chained reasoning and decisions

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

**Analysis:** This is not a stick structure made up of closed regular shapes of triangles or squares. The fish has its **body components made up of specific sticks**. In this case,

Sticks 1 and 2 make up the HEADand with 3 and 4 make up the HEAD and the BODY. The TAIL-FINS are made up of sticks 7 and 8 and the two BODY-FINS by sticks 5 and 6.

Observe that the **only closed component** is the HEAD and the BODY made up of four sticks.

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

moving 4 sticks.

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.

As you have to move minimum number of sticks, the constraint really controls your every stick selection and movement. 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 of the fish puzzle structure and clear unambiguous reasoning. Once you are confident that it is true, rest follow easily.

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

We would have been left with only 1 stick move and the tasks of reforming the tail-fins and body-fins. An impossible task.

So it follows,

You have to

form the new closed square by one stick move with other three sides of the square already in place, a nearly complete square.

We show you the numbered fish again but with important sticks colored. This will make visualization and understanding much easier.

The **only nearly complete square structure with three sides is formed by sticks 4, 6 and 8**. Its single open side is to be closed by 1 stick move. **That is a certainty** and the only possible way to form the HEAD and BODY turned around in a single stick move.

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

We take up **analytical reasoning along a fail-safe certain path**. 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?

Now **we select stick 1 with confidence**, because at this stage itself we could identify the **stick 2 to be one of the two new tail-fins already in place**. We cannot disturb it. This fin identification is possible as we have mentally formed the new head and body.

This is **chained reasoning.**

We show you the stick 1 moved to its new position to form the new head and body.

In addition we would show the rest of the two sticks to be moved colored for easy explanation.

At this stage it is dead easy to identify **stick 3 to be 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. We have colored the two differently. One will form the second tail-fin and the other, the second body-fin, with no specific choice or sequence of movement.

**Vital was the first stick movement.**

The finished turned around fish is shown below.

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

### End note

We have approached the problem **systematically and analytically, and not in any random way, **asking a series of questions and forming the answers after analysis. The possibilities gradually narrowed down and homed in to the solution unerringly.

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.

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