Solve matchstick puzzle move 4 to make 10 squares in 5 mins. Each matchstick must be attached to a square in the solution figure. Think systematically.

### The matchstick puzzle move 4 to make 10 squares

In the figure below move 4 matchsticks to form 10 squares that can be of different sizes. The squares may not even be on the same plane. But all matchsticks must form a side of a square.

**Time to solve the puzzle:** 5 mins.

Try out all by yourself to enjoy the brain-twist element of the puzzle.

### Solution to the matchstick puzzle move 4 to make 10 squares

We don't have to ensure that the squares are of same size. Taking this cue, we count the total number of squares in the puzzle figure itself as below.

In the puzzle figure, same size squares are 4 and there is an additional larger square formed at the outer boundary with sides 2 matchsticks long.

The main hurdle is - **how can we increase the number of squares from 4 to 10!**

It is clear from the small number of 12 matchsticks that **it will be impossible to rearrange these 12 matches to form 10 squares of same size.**

This is because 10 independent squares would require 4 x 10 = 40 matches and maximum number of common matches in 10 squares can be around 13. Reducing 13 from 40 we get 27 that is a close estimate of the minimum number of matches required to form 10 squares of same size adjacent to each other.

We draw the inevitable conclusions,

Conclusion 1:To form 10 squares out of 12 matches in the given figure, we have to create largest number of small squares possible with rest smaller number of larger squares.

Conclusion 2:In other words,we have to find a way to convert one or more than one of the four squares in the puzzle to a figure consisting of smaller squares.

Right at this point the first key idea clicked in our mind,

Why!

The puzzle figure itself is an example of how we can convert a large square into 5 squares, 4 small and 1 large.

Only difference would be - we will convert one of the four smaller medium sized squares to 4 still smaller squares plus the 1 medium sized square.

We'll get then 5 squares from 1 medium sized square.

Without any further analysis, we proceed to act as we thought. The resulting figure is shown below.

The faded out two matches are the two matches moved cross-wise.

How many squares do we have now? It is only 6. We could increase the number from 5 to 6 only, by moving two matches.

Looking at this result of the experiment, the next important conclusion follows naturally,

Important conclusion 1:As two 5s make 10, if we can form two squares as in the above figure each into 5 square units, we will have straightway 10 squares.

But would really be so easy? Don't we need think deeper?

Now we remember the basic concept of matchstick puzzles - **every common stick between two squares reduce the number of sticks needed to form independent squares by 1.**

This is the so familiar **common stick concept.**

Following figure makes it very clear.

For two independent squares with no common stick, 8 matches are just sufficient. But this number is reduced to 7 because of the 1 common stick in the figure on the right.

This means **we cannot straightway form two numbers of 5 square units like above.**

Important conclusion 2:Forming two 5 square units by moving 4 matches is the way to go, but thetwo units must be corner-connected having no common sides.

Following is an example of two 5 square units having a common side. **This solution is invalid** because of the hanging unattached crossed-out stick on the right.

This error has happened because of wrong choice of two pairs of matches to be moved as well as the squares onto which the pairs were to be moved.

As we know now the stringent rule of forming the two 5 square units with no common stick between the two, we don't have to worry about the sticks that are to be moved. Those automatically would turn out to be the **two pairs of corner sticks.**

Following is the final solution,

The two pairs of corner matches that are moved are faded out in the figure.

8 squares are small and two are medium sized making 10 squares in total. The large outer square is destroyed in the process.

Observe that we have taken the steps with clear intent and after analysis taken the next step always moving towards the solution. This is systematic problem solving.

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