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.

This Coffee Puzzle Harder Than You Think!

With all credits to the creator of this picture puzzle, here it is just reproduced once again. 

So what do you think, which coffee cup will fill up first?

Hint : Don't conclude early!

 Coffee Cup Puzzle

This should be the first one!

 

Only This Cup Will Fill Up!

Purpose of the title of the post!

If you think that cup 4 will fill up first then you are deceived by the creator successfully.  You might have found the order of filling cups as 4,9,7 & 5. Congrats, your brain hasn't processed details! Didn't you notice the blocks? 

   Coffee Cup Puzzle

Would You Help This Farmer ?

A farmer had 25 cows. To identify easily he numbered them from 1 to 25. Interestingly, each cow produces liters of milk equal to the respective number given. For example, a cow numbered 5 gives 5 liters of milk or a cow numbered 18 produces 18 liters of milk. Now that farmer had 5 sons. Farmer wants to share those 25 cows among his 5 sons with each son getting 5 cows. But he wants to make sure each son would get equal amount of milk.

How should he make 5 groups of cows to distribute among his sons?

Please, Help me!

This is what farmer need to do! 

Fair Distribution of Farmer's Cows

What was the interesting?

First let's name 5 sons as A,B,C,D & E. Now look at the image below.

Just collect numbers surrounded by same shapes. If you observe carefully answer, a difference of 4 created at one place which is compensated at other 4. Each son would be getting 65 liters of milk.

Fair Distribution of Cows