Question

I have a site that requires random mathematical problems to be generated based on 3 parameters: operator (addition, subtraction, multiplication, division), regrouping (to carry or not to carry), and columns (one or two). I’ve been trying to wrap my head around how to go about doing this, but everything I come up with has a flaw in some way or other.

Here is what I am working with currently:

function create_problem($operator, $regrouping, $columns){
    $top = rand(1,9);
    $bottom = rand(1,9);

    if($operator == "+"){
        if($columns == 1 && $regrouping === false){
            $result = array(
                'top' => $top,
                'bottom' => $bottom,
                'formula' => "$top.$operator.$bottom"
            );
        }
        if($columns == 2){
            if($regrouping === false){
                if($top+$bottom > 9){
                    $diff = ($top+$bottom)-10;
                    $top = $diff+rand(1, 3);    
                }
                $result = array(
                    'top' => $top,
                    'bottom' => $bottom,
                    'formula' => "$top.$operator.$bottom"
                );
            }else{
                if($top+$bottom < 10){
                    $top = rand(1, $bottom+1);
                }
            }
        }
    }
    return $result;
}

If anyone has dealt with this, or if anyone has any pointers, I would be most appreciative!

Answer 1

this function first checks for regrouping, and produces random numbers so that the sum of common-column numbers are less than 10 (for no-carry) or greater or equal to 10 (for carry).

function create_problem($operator, $regrouping, $columns){
$x1 = '';
$x2 = '';
$y1 = '';
$y2 = '';
if ($regrouping){
    if ($columns == 2){
    $x1 = rand(1,9);
    $x2 = rand(0,9);
    $y1 = rand(9-$x1,9);
    $y2 = rand(10-$x2,9);
    } else {
    $x1 = rand(1,9);
    $y1 = rand(9-$x1,9);
    }
} else {
    if ($columns == 2){
    $x1 = rand(1,8);
    $x2 = rand(0,8);
    $y1 = rand(1,9-$x1);
    $y2 = rand(0,9-$x2);
    } else {
    $x1 = rand(1,8);
    $y1 = rand(1,9-$x1);
    }
}

return $x1.$x2.$operator.$y1.$y2;
}

ex..

31
+54

..where
3=$x1
1=$x2
5=$y1
4=$y2