Sunday, January 19, 2014

How many squares are there in n X n box



How many squares are there in n X n

How many squares are there in a chess board?
Have you counted yet?

When I was at class VII.I counted and it was maybe 204.

At high school, it just tested the formula below and it worked.

So, chess board has 204 squares.

Formula is   
Sum of squares of natural numbers =        n(n+1)(2n+1)
                                ------------
                                      6
where n= number of box in row or column

No. of box in row or column (n)                    Sum of squares
1                                            1
2                                            5
3                                            14
4                                            30
5                                            55
6                                            91
7                                            140
8                                            204
9                                            285
10                                            385

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