## The 7 squares matchstick puzzle should be easy if you apply reasoning based on matchstick puzzle concepts

The 7 squares matchstick puzzle: Move 2 matches to make 7 squares in the puzzle figure. Time 10 mins. Apply reasoning based on matchstick puzzle concepts.

#### The 7 squares matchstick puzzle

In the matchstick puzzle figure, move 2 matches to make 7 squares with each matchstick part of a square and no stick kept hanging.

**Time to solve:** 10 minutes.

First, try to solve yourself in your own way. It is quite possible that you would be able to solve this not so difficult stick puzzle within 10 minutes.

Our solution follows a step by step reasoning approach to arrive at the answer figure quickly with minimum guessing attempts. *It is based on a problem solving and innovation model.*

### Move 2 matches to make 7 squares matchstick puzzle: First stage of solution to specify actions

#### Problem analysis and selection of most suitable technique

In solving a matchstick puzzle (or solving any puzzle or problem), you would decide first which technique (or strategy) would be most effective in solving the puzzle. This decision would invariably be based on **broad and quick analysis of the problem** evaluating the strategy or technique that would produce best results.

This is the important first stage of any systematic approach to problem solving.

For this puzzle, based on matchstick concepts (we assume you have some experience) you would draw your conclusions quickly,

- The
**Common stick analysis technique**won’t be effective for this puzzle, as this has*many squares of different sizes with few common sticks.* - You won’t also use the
**End state analysis technique**of comparing the possible final figure and the puzzle figure to select the possible final figure having maximum similarity with the puzzle figure.*This is because, visualizing the possible final figures itself is not an easy task here.*

But yes, you can analyze the number of closed shapes at start and at end. This is **the shape analysis technique.** *You select it as the most appropriate approach for this puzzle.*

It is easy to draw the** first conclusion** from this analysis,

The target figure would have 7 squares—an increase of 2 squares from the puzzle figure.

And the **first action you can specify** from the puzzle description as,

To create 2 more new squares in 2 stick moves, effectively you have to create 3 new squares by moving 2 sticks.

The **reason behind this action requirement is**—by moving 2 sticks you would destroy at least 1 square, and so you have to create 3 new squares to create 7 squares in the final figure.

Now you realize that by moving 2 sticks, you might destroy 2 squares, not 1. In that case, you would have to create 4 new squares by moving two sticks. And it would be infeasible to create 4 new squares in 2 stick moves.

With this realization, you define the stick movement action requirement more stringently as,

To create 2 more new squares in 2 stick moves, you would destroy just 1 square and create 3 new squares by moving the 2 sticks.

**Till now** you have analyzed the puzzle broadly and drawn the conclusions without looking at the puzzle figure.

The conclusions and action requirements would be true for any matchstick puzzle that requires an increase in the number of closed shapes by 2 in 2 stick moves.

This is why the **shape analysis technique is ABSTRACT** and hence has more power and applicability.

Now *you set to analyze the puzzle figure in details and realize that some sticks are like each other regarding their positions in the structure of sticks.*

### Move 2 matches to make 7 squares matchstick puzzle: Second stage of solution to narrow down stick move analysis

#### Analyze given puzzle figure to Classify types of sticks for movement

A **natural technique** that is used in many problem situations is **Classification into equivalent types technique.**

With the awareness that **some sticks occupy exactly the same equivalent positions in the figure**, you decide to apply this powerful technique on the puzzle figure.

If you study the effect of moving any of these sticks of equivalent positions, you would know what would happen if you move any other stick equivalent to the stick you have studied. Effectively, by testing one stick in an equivalent class you study all sticks in the class—a great reduction in time to test.

**Note:** *Technical name for these equivalent classes is Equivalence Classes.*

Positional equivalence of sticksis theclassification criterionfor this puzzle figure.

The following figure shows classification of the sticks into equivalent types.

So you **divide the sticks in three independent and equivalent class types** to study the results of moving the sticks in each type,

**Class type A: 4 pairs of CORNER sticks of the large outer square: 1 pair labeled as A1, A2:**

You cannot move any of these pairs because by moving a pair of corner sticks, you would destroy 2 squares—the corner square and the large outer square. This would violate the specific requirements you have drawn by shape analysis. These 8 sticks are identified as invalid for further analysis.

**Class type B: 4 sticks on the MIDDLE of the 4 sides of the large outer square: 4 labeled as B1, B2, B3, B4:**

If you move any two of the four, you won’t violate the shape analysis requirement (you would destroy just 1 square). But if you move 2 of these 4 sticks, you would also create two hanging sticks unattached to any square. This violates the second requirement of the puzzle description. These 4 sticks also are identified as invalid.

**Class Type C: 4 pairs of INSIDE CORNER sticks of the large outer square: 1 pair labeled as C1, C2:**

Moving such a pair destroys just 1 inside corner square. It does not create any unattached hanging sticks to be taken care of later. So you are sure that you would solve the puzzle by moving any pair of these 4.

With sticks identified for movement, the only task remains is—finding the places for the sticks moved.

### Move 2 matches to make 7 squares matchstick puzzle: Third stage of Solution

#### Analyze possible places for moving 1st stick and the 2nd stick for final solution

At this final stage, you further breakdown the problem for **analysis of 1st stick move** and then the** 2nd stick move** and try out places where each stick can be moved to create the solution figure of 7 squares.

This is the natural way of moving the sticks. Isn’t it?

But before you start the trial, even at this late stage, you **decide to apply shape analysis on the number of squares again.**

To create 3 new squares by the 2 moves,

When you move the first stick and destroy 1 corner square you must create at least 1 new square. As creating 2 new squares by the first stick move is impossible here, you would specify the requirement as—you MUST create 1 new square.

Now you would get down to identifying the feasible promising options where you can place the just moved 1st stick.

The following figure shows the two feasible promising place P1 and P2 for the 1st moved stick.

First stick C1 can be moved to any of these two. Move it to P1 and create the new square A.

With the help of shape analysis again, now you can easily specify the strict requirement for the second stick move,

By the second stick move, you won’t destroy any square, but you

MUST create two new squares.

**Question is:** how can you create two new squares by one stick?

**Answer is clear:** You would choose one of the remaining feasible place options identified in the 1st stick move so that an additional NEW SQUARE of size larger than the small squares but smaller than the large outer square is created.

**Solution is easy**—remaining place option is just 1.

Move stick C2 to place P2. Two new squares B and C are created.

The following shows the final solution figure.

Here, solving of the puzzle has not been the only goal—the goal was to **solve it with minimum guesses or trials, following a systematic and reasoned approach.**

If you are curious, you may go through the possible representation of a model for general problem solving and innovation. You would find the process of solution for the puzzle similar to this model.

### A feasible model for general problem solving and innovation

**Step 1: Problem definition in precision:** Many times, especially in real life problems, this stage of understanding clearly what the problem is takes time, effort and will. For the puzzle, the problem is already precisely defined.

**Step 2: Problem analysis and selection of strategy:** With an overall brief analysis of the problem, identify appropriate strategy and resources that you will use for solving the problem.

**Step 3: Taking actions:** According to the strategy, when you analyze the problem more thoroughly and take actions for a solution, you would identify the main barrier to the solution. You would also identify patterns and techniques to overcome the barriers.

**Step 4: Fine tune strategy and techniques:** In this step, you may feel the need to repeat stage 1 to 3 by having a re-look at the strategy selected and tune it.

**Step 5: Reach a few possible solutions:** After going systematically through the steps, you will either reach the solution OR identify a small set of possible solutions.

**Step 6: Trial coupled with new way of thinking: **Reach the most desirable solution by planned study and innovative breakthrough ideas with the help of trial on the set of possibilities.

*Innovation is inseparable from problem solving.*

Throughout the stages, without innovative new way of thinking, the most desirable least cost solution may never be reached.

### Know how to solve difficult problems easily without wasting time on random attempts

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