Prized Quiz 2

Hi Guys, Welcome Back To Second Edition Of Prized Quiz.

Today, i.e. 11th September, I was at library in the evening. I thought a question myself and got the answer in few minutes. It is simple question, hence no big prize though. Question has two parts 'a' and 'b'. The answer required is a general one. The question is as follows :-

PART (A)

• Suppose there is a matrix of dimension m*n, where m>0 and n>0.

• Find out the number of rectangles that can be formed of exactly x*y size, where x>0,y>0 and x<=m,y<=n.

• Find the answer in terms of m,n,x,y.

PART (B)

• Suppose there is a matrix of dimension m*n, where m>0 and n>0.

• Find out total number of rectangles that can be formed. i.e. All possible Dimensions.

• Find the answer in terms of m,n.

Prize: Treat at Cafe.

Mail all your answers at navdeep983879@gmail.com with subject as PRIZED QUIZ 2.

Deadline: First One To Answer Both Parts.

Note: Write all Your queries in Comments Section. Do Not Write Answer There.

A Prized Quiz

Hi Guys, Today I was attending a lecture in the morning. There a question came to my mind. And I wanted to come up with a general answer. The question was :-

• Let us take a number 'n', such that n>0.

• Now make an n*n matrix.

• Fill it with distinct numbers ranging between 1 and n^2. Every number used exactly one time.

• The sum of elements of each individual row, sum of elements of each individual column and sum of elements of each individual diagonal must be same.

I wanted to solve it for any natural number.

Well I succeeded for odd numbers.

i.e. My algorithm works for 1,3,5,7,9,11,...,(2m+1) where m>=0

Now, my question is that, can u do it for even numbers?

You can solve this question for me in two different ways

1. Sovle for any particular case, like n=4 or n=6 or so on.

Prize: Treat at Cafe.

Eligibility: Any JUITian can answer.

2. Solve it for any general case n, where n>0 and divisible by 2.

Prize: Treat at Moksh or Paradise or Destination or any where in Simla/Solan.

Eligibility: Anyone can answer.

A Hint: The sum must be (n^3 + n) / 2

Mail all your answers at navdeep983879@gmail.com with subject as PRIZED QUIZ

Deadline: A week after the first correct answer is submitted (This will be updated as soon as I get correct answer).

Correct Answers Yet: None

Note: Write all Your queries in Comments Section.

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