CHESS1 - Editorial

number-theory

#1

PROBLEM LINK:

Practice

Contest

Author: Md Shahid

Tester: Arkapravo Ghosh

Editorialist: Md Shahid

DIFFICULTY:

SIMPLE

PROBLEM:

Given N.You need to find the number of possible squares in N x N chess board.

EXPLANATION:

In this problem you have to count total numbers of all possible squares in the given N X N grid chess.




Total number of square in 1 X 1 chess = 1.


Total number of square in 2 X 2 chess = 5.


Total number of square in 3 X 3 chess = 14.




Can you see a pattern in the above three lines?

Yes.




Total number of square in 1 X 1 chess = 1 = 1^2.


Total number of square in 2 X 2 chess = 5 = 1^2 + 2^2.


Total number of square in 3 X 3 chess = 14 = 1^2 + 2^2 + 3^2.


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.


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Total number of squares in N X N chess = 1^2 + 2^2 + 3^2 + . . . . . . . . + N^2




As we know from algebra,




1^2 + 2^2 + 3^2 + . . . . . . . . + N^2 = (N(N+1)(2N+1))/6

Input N
Sum = (N(N+1)(2N+1))/6
print Sum

AUTHOR’S, TESTER’S AND EDITORIALIST’S SOLUTIONS:

Author’s and editorialist’s solution can be found here.
Tester’s solution can be found here.

Tags:- ENCODING CHESS1 dshahid380