## Matchstick puzzle: Move 2 sticks to make 5 matchstick shapes

Move 2 sticks to make 5 matchstick shapes of squares, triangles or rhombuses. How many such new figures can you make?

**Total recommended time** 10 minutes. No matchstick moved can be placed in a position of an already moved stick.

Try solving the puzzle. It will be interesting we can assure.

### A Bonus Puzzle

With the experience of solving the first puzzle it should be easy for you to solve this variation.

#### Second puzzle of Move 2 sticks to make 5 matchstick shapes (puzzle figure differs from the first)

**The Puzzle:** In the puzzle figure below, Move 2 sticks to make 5 matchstick shapes. The shapes must be non-overlapping and no matchstick moved can be placed in a position of an already moved stick. How many such solutions can you find?

#### Comment

This is the **second puzzle** having the same **mixed matchstick shapes of a triangle, two squares and a rhombus.** If you haven’t solved the first such puzzle you may try it here.

Because of the mixed matchstick shapes, it is not useful to apply the End state analysis technique on the possible puzzle solution figures that we have used so effectively in solving the puzzle, Move 2 sticks to make 4 squares matchstick puzzle.

Also, our usual method of analyzing the number of sticks together with common sticks required are of **little use here.**

To solve this puzzle instead, we will use,

- the most basic matchstick puzzle concepts,
- analysis of the number of matchstick shapes,
- refining requirement specification, and,
- step-by-step reasoning.

Concepts for solving mixed shape matchstick puzzle follows.

### Concepts needed to solve the mixed matchstick shapes puzzles

#### Common stick properties

A common stick between two closed shapes,

- destroys two regular matchstick shapes
**if removed,** **reduces**the need for the number of sticks to form the two matchstick shapes independently**by 1.**

#### Diagonals of a square and a rhombus

In a regular shape like a rhombus A in the puzzle figure shown below, you can place a stick as the shorter diagonal to divide the rhombus into two triangles, increasing the number of closed shapes by 1.

**Note:**

Geometrically, the shorter diagonal divides a rhombus into two equilateral triangles. But you won’t use any geometry or math concepts to solve matchstick puzzles, isn’t it?

You’ll just try out the possibility by actually placing a stick to connect two nearer corners of the tilted four-sided closed shape and check for yourself whether you have got two triangles.

But you can’t use a stick as the diagonal of a square because a diagonal is always longer than any of its sides in a square.

#### Two triangles can form a rhombus but not a square

As you can place a stick as the shorter diagonal in a rhombus, effectively you combine two triangles to form a rhombus. But you cannot combine two triangles to form a square.

These concepts you can understand just by creating the shapes with sticks. You don’t really need any geometry background.

We will now solve the puzzle systematically by step-by-step reasoning.

### Solution to Move 2 sticks to make 5 matchstick shapes puzzle

#### Stage 1: Identify two sticks that can be moved: Analysis of requirements—Make initial conclusions

The puzzle figure with the sticks and shapes labeled is shown below for easier reference to the components.

The three common sticks are specially identified by tick-marks and are not numbered.

From the problem description, the **first conclusion** can be made straightaway,

Moving 2 sticks, you have to

destroy one and only one closed shape and create two new closed shapesto make the number of closed shapes 5 from 4.

This first conclusion is the outcome of the **analysis of the number of shapes.**

*Think over to verify the truth or falsity of this conclusion.*

An immediate **second conclusion** can be made is,

You cannot move any of the three common sticks as moving such a stick will create 4 hanging sticks at one go that would be completely unmanageable.

With these two conclusions, the choices of the two sticks that can be moved are narrowed down.

#### Solution Stage 2: Move 2 sticks to make 5 matchstick shapes Matchstick puzzle: How to create the 2 new closed non-overlapping matchstick shapes

You have reached the heart of the problem.

*Make an experiment.*

**Pick up** sticks 4 and 5. You have destroyed 1 shape as expected.

**Now you have to place** these two sticks to create 2 non-overlapping new shapes.

*Can you do it?*

Try as you may, you won’t be able to do it. This is an infeasible action that won’t lead you to the solution.

Let us *abandon this path of picking up any pair of sticks and then try to place the sticks.*

**Instead,** focus on **how to create the two new shapes** assuming that you have already selected two sticks to move.

This is a **strategic approach to problem solving** adopting the *most promising path of analysis and action.* This would lead you to the solution faster.

Now, as you are forced to think how you will create the two new shapes with 2 moved sticks, you are in the right position to make the **third conclusion** with confidence,

With each stick moved, 1 new shape has to be created to finally create 2 new shapes with 2 free sticks moved.

You are gradually refining the requirements and as a result narrowing down the possible actions.

#### Solution Stage 3: Move 2 sticks to make 5 matchstick shapes Matchstick puzzle: Applying the precise requirement rules on the puzzle figure

The crucial question to answer now is,

With 1 stick how can you create a new shape, that too twice?

For convenience, the labeled puzzle figure is shown again,

With requirements of creating a new shape strictly defined, it is easy now to identify the **ONLY one such possibility,**

First shape creation:Place a stick to complete the triangle withstick 1 and stick 5 as the existing other two sides.

Second shape creation:Place a stick as theshorter diagonal of the rhombus Ato divide it into two triangles.

**Note:** To avoid counting the rhombus also as a closed shape, the “non-overlapping” condition was included in the puzzle description.

*So you have created two new shapes with two already moved sticks, and this is the only single such possibility.*

But you haven’t yet solved the puzzle fully. One more step is still to be taken to complete the solution. **You have to identify the two sticks to move.**

#### Solution final stage: Move 2 sticks to make 5 matchstick shapes Matchstick puzzle: Identifying the 2 sticks to move

**Analysis:** As stick 5 **has to be used** in forming one of the two new shapes,** the square B cannot be disturbed at all.**

This is the reason your initial attempt starting with stick 4 and 5 failed.

It is now easy to identify **stick 8 and stick 9 to move** to form the two new shapes. The solution figure is shown.

### Solution of puzzle Part II: How many ways can you form such 5 closed matchstick shapes

With the knowledge you have gained, solving the second part of the puzzle should take just a few seconds,

Move stick 6 and stick 7to form the two new shapes.

The second solution figure is shown.

Because of the precise conclusions you have made step by step, you could be sure that these are the only two solutions possible.

### Solution to Move 2 sticks to make 5 matchstick shapes bonus matchstick puzzle

**Puzzle:** Move 2 matches to make 5 non-overlapping closed matchstick shapes. How many such solutions can you find?

#### Solution

One possible solution is shown.

With you experienced now, *we leave you to find ALL the possible solutions.*

#### End note

Solution of a puzzle by step-by-step reasoning may diminish the joy of the discovery of the solution in whatever-possible-way-I-can-solve attempts.

That’s why we strongly recommend that you should try to solve the puzzle all by yourself in your own way first and then only go through the reason-based solution to enjoy the best of both worlds,

A combination of intuitive and reason-based solution approach should produce a very satisfying overall experience.

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

*Our ebook on puzzle solutions by innovative methods will show you just that.*

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