# Thread: Compute every combination of 6 numbers

1. Registered User
Join Date
Nov 2017
Posts
3

## Compute every combination of 6 numbers

I'm more of a media developer and not the best coder, but I find myself needing to learn javascript better. I'm creating a math card game where the human player and the automated player are each dealt 6 cards. Each player must combine (concatenate) three of the cards to make a top number and the other three for the bottom number. Those two numbers are then subtracted. For the automated player, I have to go through ever possible combination of the six cards, so when the two numbers are subtracted, it gets as close as possible to a target number. I'm not very good with arrays, so I started testing every possible combination and then comparing which one was closer (See example below). This is a very inefficient way of coding this, but I'm just not sure how to do it otherwise. Any help would be greatly appreciated.

The variables have already been declared.

alienTopNum = "" + alienNum1 + alienNum2 + alienNum3;
alienBottomNum = "" + alienNum4 + alienNum5 + alienNum6;
oldDiff = targetNum - (alienTopNum - alienBottomNum);
player.SetVar("AC1R1", alienNum1);
player.SetVar("AC2R1", alienNum2);
player.SetVar("AC3R1", alienNum3);
player.SetVar("AC4R1", alienNum4);
player.SetVar("AC4R1", alienNum5);
player.SetVar("AC4R1", alienNum6);
player.SetVar("ATR1", alienTopNum - alienBottomNum);

alienTopNum = "" + alienNum1 + alienNum2 + alienNum3;
alienBottomNum = "" + alienNum4 + alienNum6 + alienNum5;
newDiff = targetNum - (alienTopNum - alienBottomNum);
if (Math.abs(newDiff) < Math.abs(oldDiff)) {
oldDiff = newDiff;
player.SetVar("AC1R1", alienNum1);
player.SetVar("AC2R1", alienNum2);
player.SetVar("AC3R1", alienNum3);
player.SetVar("AC4R1", alienNum4);
player.SetVar("AC4R1", alienNum6);
player.SetVar("AC4R1", alienNum5);
player.SetVar("ATR1", alienTopNum - alienBottomNum);
}

etc....

2. I think you are looking for Combination of 6 numbers, 3 at a time. The pattern you need to generate looks like this:
111000
110100
110010
110001
101100
101010
101001
100110
100101
100011
011100 etc. to a total of 20 possible combinations. The first 1 can vary from position 0 to 3, the next from the first position + 1 thru 4, and the last from the second + 1 thru 5.
Going through your array of card values if you find a 1 at the corresponding location, add its value to your first sum, else add it to the second sum. If the absolute value of the difference is less than any other combination, save it.
HTH

3. Registered User
Join Date
Nov 2017
Posts
3
Thank you for your feedback wbport. It's very appreciated. For what I'm trying to do, I believe there are actually 720 combinations. There are a total of six numbers and those numbers can each range between 0 and 9. I'm taking three of those numbers and subtracting the other three. For instance:
788
- 432

I guess if the two 8s were swapped out in this scenario, those would be the same thing, so the possible combinations are a bit less than 720. So, in theory, I know I need to place every possible combination into an array, test to see which combination, when subtracted, gets closest to the target number, and also account for == results (more than one combination results in the same difference from the target number).
I hope that helps clarify my needs. I'm just not sure how to go about doing it.

4. This is going be very difficult if you don't use arrays. At any rate you need an algorithm for creating all 720 (6!) permutations of your dealt cards. Search for "javascript permutation algorithm".
Last edited by wbport; 11-30-2017 at 04:55 PM.

5. Registered User
Join Date
Nov 2017
Posts
3
Thank you. I'll look into that.

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