Make 7 Using 5 !

In the given picture, you can see that there are two matchsticks that have been used to create five squares. You are allowed to move just two matchsticks and must form seven squares. You can't overlap the matches and you are not allowed to break them. Also, like you can see in the picture, all squares must be closed. 

That's how it can be done!

Steps to Make 7 from 5

What was the challenge?

All we need to do is to re place these 2 match sticks.

So we get,

A Mathematical Clue From The Merchant

A rich merchant had collected many gold coins. He did not want anybody to know about them. 

One day, his wife asked, “How many gold coins do we have?”

After pausing a moment, he replied, “Well! If I divide the coins into two unequal numbers, then 32 times the difference between the two numbers equals the difference between the squares of the two numbers.”

The wife looked puzzled. Can you help the merchant’s wife by finding out how many gold coins they have?

Here are mathematical steps to find those!

Using The Mathematical Clue

What was that clue?

Since when divided into 2 unequal numbers difference won't be 0. Let x and y be the 2 unequal numbers.

As per merchant,

32 (x - y) = x^2 - y^2

32 (x - y) = (x - y) (x + y)

Dividing both sides by (x - y) which is non zero as x is not equal to y,

32 = x + y

x + y = 32.

Let's verify with x = 30 and y = 2. So 32 (x - y) = 32 ( 30 - 2) = 896. And x^2 - y^2 = 30^2 - 2^2 = 900 - 4 = 896.

Hence, Merchant had 32 coins in total.

Squares From Squares Challenge

In the picture that is attached with this question, you can find a square which comprises of four little squares inside it. Consider this square to be made with matchsticks. You have to remove two matchsticks such that only two squares remain instead of five.How will you do it ?

Make it 2!

Challenge accepted here! 

Source 

Squares From Squares Challenge Accepted

What was the challenge? 

All that you need to do is that remove these 2 match sticks labelled in figure below.

So we get exactly 2 squares as below.