Function to count how many numbers are there with the digits and division value specified

Question

I started making a function that will be able do the following: Count how many 6 digit numbers you can make with the digits 0,1,2,3,4 and 5, that can be divided by 6?

How I currently try to start, is I make an array of all the possible numbers, then take out every number that has any of the numbers' arrays elements in it, then remove the ones that are not dividable with 6.

I got stuck at the second part. I tried making 2 loops to loop in the array of numbers, then inside that loop, create an other one for the length of the allnumbers array to remove all matches.

Then I would use the % operator the same way to get every element out that doesn't return 0.

The code needs to be flexible. If the user asks for eg. digit 6 too, then the code should still work. Any way I could finish this?

My Code is:

var allnumbers = [],j;
var biggestnumber = "999999999999999999999999999999999999999999999999999999999999";

function howmanynumbers(digits,numbers,divideWith){
    if (digits && numbers && divideWith){
        for (var i = 0; i < 1+Number(biggestnumber.substring(0,digits)); i++ ){
            allnumbers.push(i);
        }

        for (j = 0; j < numbers.length; j++ ){
            var matchit = new RegExp(numbers[j]);
        }
            //not expected to work, I just had this in for reference
        if ( String(allnumbers[i]).match(matchit) != [""]){
            j = 0;
            allnumbers.splice(i,1);
            var matchit = new RegExp(numbers[j])
        }
    }
    else {
        return false;
    }
}

Answer 1

This is my take on the entire solution:

var i;
var allowedDigitsPattern = /^[0-5]+$/i;
var numbers = [];

for (i = 100000; i < 555555; i++) {
    if (allowedDigitsPattern.test(i.toString())
        && i % 6 === 0) {
        numbers.push(i);       
    }
}

And you can look at your results like this:

document.write('There are ' + numbers.length + ' numbers<br>');

// write out the first ten!
for (i = 0; i < 10; i++) {
    document.write(numbers[i] + '<br>');
}

Update based on comments...

The configurable version of this would be:

var i;
var lowestDigit = 0;
var highestDigit = 5;
var numberOfDigits = 6;

var allowedDigitsPattern = new RegExp('^[' + lowestDigit + '-' + highestDigit + ']+$', 'gi');

var smallestNumber = '1';
for (i = 1; i < numberOfDigits; i++) {
    smallestNumber += '0';
}

var biggestNumber = '';
for (i = 0; i < numberOfDigits; i++) {
    biggestNumber += highestDigit.toString();
}

var numbers = [];

for (i = smallestNumber; i < biggestNumber; i++) {
    if (allowedDigitsPattern.test(i.toString())
        && i % 6 === 0) {
        numbers.push(i);        
    }
}

document.write('There are ' + numbers.length + ' numbers<br>');

You need to change the smallest and largest numbers based on the configuration. I have made both the allowable digits and the length of the number configurable.