# 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 = $14$ = $1^2$ $+$ $2^2$ $+$ $3^2$.

$.$

$.$

$.$

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

asked
**09 Oct, 01:10**

3★dshahid380

20●3

accept rate:
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