Question

How to find the number of squares in an N*N grid with PHP

Answer 1

/*
Total squares in a 3 * 3 grid are 14

1x1 squares = 9 Squares
2x2 squares = 4 Squares
3x3 squares = 1 Squares
*/

function countSquaresInNxNGrid($N) {
    // Formula: Total Squares = N * (N + 1) * (2N + 1) / 6
    return ($N * ($N + 1) * (2 * $N + 1)) / 6;
}

$N = 3;

// Validate input
if ($N <= 0) {
    echo "Grid size must be a positive integer!\n";
    exit(1);
}

$totalSquares = countSquaresInNxNGrid($N);

echo "The total number of squares in a {$N}x{$N} grid is: {$totalSquares}\n";



/*
run:

The total number of squares in a 3x3 grid is: 14

*/

 

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