Algorithm that generates all versions of an array with possible weights assigned 0-100

Theres probably a better way, but heres my attempt:

$result=array(); // Empty array for your result
$array=range(1117,7777); // Make an array with every number between 1117 and 7777
foreach ($array as $k=>$v) {  // Loop through numbers
    if ((preg_match('/[890]/',$v) === 0) && (array_sum(str_split($v, 1)) === 10)) { 
        // If number does not contain 8,9 or 0 and sum of all 4 numbers is 10
        // Apply function to multiply each number by 10 and add to result array
        $result[] = array_map("magnitude", str_split($v, 1));
    }
}
function magnitude($val) { // function to multiply by 10 for array map
    return($val * 10);
}
print_r($result);

Working demo here

EDIT

Sorry I realised my code explanation isn't totally clear and I condensed it all a bit too much to make it easy to follow.

In your example the first array would contain (10,10,10,70). For the sake of simplicity I divided everything by 10 for the calculations and then just multiplied by 10 once I had a result, so your array of (10,10,10,70) becomes (1,1,1,7). Then your final array would be (70,10,10,10) which would become (7,1,1,1).

My approach was to first to create an array containing every combination of these four numbers, which I did in two steps.

This line $array=range(1117,7777); creates an array like this (1117, 1118, 1119 ... 7775, 7776, 7777) (My number range should really have been 1117 - 7111 instead of 1117-7777).

Applying str_split($v, 1) to each value in the loop splits each 4 digit number in the array into another array conatining 4 single digit numbers, so 1117 will become (1, 1, 1, 7) etc

As each of your items can't have a weight below 10 or above 70 we use (preg_match('/[890]/',$v) === 0) to skip any arrays which have 0,8 or 9 in them anywhere, then array_sum(str_split($v, 1)) === 10) adds up the four digits in the array and only returns arrays which total 10 (you wanted ones which total 100, but I divided by 10 earlier).

array_map applies a function to each element in an array. In my example the function multiplies each value by 10, to undo the fact I divided by 10 earlier.

When you say is it possible to alter steps, can you give me a couple of examples of other values and the output you want for them?

If you want a totally different approach and using mysql isn't a problem then this also works:

Create a new table with a single row. Insert all the values you need to check

INSERT INTO `numbers` (`number`) VALUES
(10),
(20),
(30),
(40),
(50),
(60),
(70);

Then your php looks like this

$result=array();
try {
    $dbh = new PDO('mysql:host=aaaaa;dbname=bbb', 'ccc', 'dddd');
    foreach($dbh->query('SELECT *
FROM numbers a
CROSS JOIN   // A cross join returns the cartesian product of rows
numbers b    // so every row with every combination of the other rows
CROSS JOIN
numbers c
CROSS JOIN
numbers d
ON
a.number = b.number OR a.number != b.number') as $row) {
        if (($row[0] + $row[1] + $row[2] + $row[3]) === 100) {
            $result[] = $row;
        }
    }
    $dbh = null;
} catch (PDOException $e) {
    print "Error!: " . $e->getMessage() . "<br/>";
    die();
}
print_r($result);