top button
Flag Notify
    Connect to us
      Facebook Login
      Site Registration Why to Join

    Get Free Puzzle Updates

Facebook Login
Site Registration

Proof: Total number of squares in a square?

+1 vote

If you divide any square into power (2, 2N) equal squares then total number of squares formed is sigma(power(i,2)) where i iterates from 1 to power( 2, N).

1 square has total 1,
Divided into 4 has total 1^2 +2^2
Divided into 16 equal squares has total 1^2 + 2^2 + 3^2 + 4^2
Divided into 64 equal squares has 1^2 + 2^2 + 3^2 + ......... + 8^2

Can you prove if this is correct? I have solved it.

posted Jun 23, 2014 by Hariom Sharma

Share this puzzle
Facebook Share Button Twitter Share Button Google+ Share Button LinkedIn Share Button Multiple Social Share Button

1 Solution

0 votes

Total number of squares are defined as

1^2 + 2^2 + 3^2...n^2 or n*(n+1)(2n+1)/6

Assumption square is divided equally using (n-1) horizontal and (n-1) vertical lines.

You can always prove this with induction with assuming the above statement is true for the n and adding one more vertical and horizontal line will get the statement is true for n+1..

solution Jun 23, 2014 by Salil Agrawal

Similar Puzzles
+1 vote

There are two whole numbers, difference of their squares is a cube and difference of their cube is a square. These are the smallest possible numbers. can you find the numbers?

0 votes

Draw five squares joined in the shape of a plus. Place distinct digits (other than 0 or 1) so that the three numbers in the vertical line multiply together to give the same answer as the three numbers in the horizontal line multiplied together?

+1 vote

On the first day, James read 20% of a book. On the second day, he read another 66 pages and discovered that he had read 80% of the unread pages. What is the total number pages of the book?

0 votes

The sum of a non zero number, its square, its cube and its four power is 7380. If five power of the number is added to 7380 and divided by the number , then what will be the qoutient ?

Contact Us
+91 9880187415
#280, 3rd floor, 5th Main
6th Sector, HSR Layout
Karnataka INDIA.