## 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 is different 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 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 number of matchstick shapes,**refining requirement specification,*and,*step-by-step reasoning*.

If you already are aware, you may skip the concepts in the following section to *move straight to the solution.*

### 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 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 it is true that the shorter diagonal divides a rhombus into two equilateral triangles. But you won't use any geometry or math concepts in solving 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 as a result.

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* using *step-by-step reasoning.*

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

#### Stage 1: Understanding which two sticks can be moved: Analysis of requirementsâ€”Making 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 shapeandcreate two new closed shapesto make the number of closed shapes 5 from 4.

This first conclusion is the outcome of **analysis of 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 as many as 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.**

**Note:**This is the reason why 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 below.

#### 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 below.

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 below.

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

### End note

Solving a puzzle by step-by-step reasoning may diminish the joy of 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 best of both worlds,

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

### Puzzles you may enjoy

#### Riddles

**Riddle of 4 persons crossing a bridge over a river at night**

**Riddle of PROBLEMSOLVING - Creation and application of Repetition pattern based technique**

#### Mathematical puzzles

**Reverse cheque puzzle solution**

**Counting eggs puzzles based on Euclid's division lemma**

**Monkey and the coconuts puzzle with solutions**

**10 digit Conway number puzzle with solution**

**World's Hardest Easy Geometry Puzzle Solved with Techniques Explained Step by Step**

**Hard Algebra Puzzles Solved by Basic Exponent Concepts and Reasoning**

**Three squares in a triangle puzzle**

**9 squares in a rectangle math puzzle**

**How many addition signs needed to make sum of 99**

#### Logic analysis puzzles

**Method based solution to Einstein's logic analysis puzzle, whose fish**

**How to solve Einstein's puzzle whose fish confidently, improved method based solution**

**Logic puzzle, When is Cheryl's birthday**

**Liar and truth-teller riddle with step by step easy solution**

#### River crossing puzzles

**Farmer with fox, goose and bag of corn crossing the river puzzle**

**Two pigs and two hens crossing river puzzle**

*3 monkeys and 3 humans crossing river puzzle*

**King queen minister washerman river crossing puzzle**

#### Ball weighing puzzles

**Find the heavier among 8 identical balls in 2 weighing puzzle**

**Find the fake ball among 8 identical balls in 3 weighing puzzle**

**Find the fake ball among 9 identical balls in 3 weighing puzzle**

**Find the fake ball among 12 identical balls in 3 weighing hard puzzle with solution**

#### Matchstick puzzles

**Solution to 6 triangles to 5 triangles in 2 moves, first matchstick puzzle**

**Matchstick puzzle 5 squares to 4 squares in 2 moves**

**Matchstick puzzle 5 squares to 4 squares in 3 moves**

**Matchstick puzzle, Turn around the fish in 3 moves**

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

**Hexagonal wheel to 3 triangles by removing 4 sticks**

**Convert 5 squares to 4 squares in 3 stick moves, third 5 square matchstick puzzle**

**Matchstick Puzzle - Make the kite nose-dive in 5 stick moves**

**Make 5 squares from 6 in 2 stick moves - 6 square matchstick puzzle**

**Move 3 sticks and convert 5 squares to 4 squares in 4th 5 square matchstick puzzle**

**Move 3 sticks and convert 4 squares to 3 squares matchstick puzzle**

**Move 8 sticks and convert 5 squares to 2 squares matchstick puzzle**

**First Move 3 sticks and make 2 squares matchstick puzzle**

**Second Move 3 sticks and make 2 squares matchstick puzzle**

**Remove 3 matchsticks to leave 6 triangles puzzle**

**Add 3 matchsticks to make 4 triangles - lateral thinking stick puzzle**

**Move 1 stick to make 4 closed shapes each with 3 or 4 sides**

**Move 2 sticks to make 5 closed shapes matchstick puzzle**

**Move 2 to make 7 squares matchstick puzzle - solution based on problem solving and innovation model**

**Move 4 to turn the tower upside down Matchstick puzzle**

**Move 2 matches to make 6 squares and move 8 matches to make 6 squares - a pair of matchstick puzzles**