TITLE: A maths number puzzle
QUESTION [6 upvotes]: We have these digits : $1,2,3,4,5,6,7,8,9$. Using these digits, we have to make two numbers such that their product must be as large as possible. We have to use all digits only once.
I did $97531\times 8642$ and got $842862902$

REPLY [2 votes]: $87531 \cdot 9642 = 843973902$
I could confirm imakesmalltalk's answer by a JavaScript program.
Install node.js, execute node the-saved-script-name.js and the last line from the program's output should be the largest possible product.
The program should run reasonably fast, it needs 3.936 seconds on my PC.
/* Create all given permutations of an array
 * @author Oriol <http://stackoverflow.com/users/1529630/oriol
 * @link http://stackoverflow.com/a/11509565/603003
 * @license CC BY-SA 3.0 with attribution required
 */
function permute(input) {
    var permArr = [],
    usedChars = [];
    function main(){
        var i, ch;
        for (i = 0; i < input.length; i++) {
            ch = input.splice(i, 1)[0];
            usedChars.push(ch);
            if (input.length == 0) {
                permArr.push(usedChars.slice());
            }
            main();
            input.splice(i, 0, ch);
            usedChars.pop();
        }
        return permArr;
    }
    return main();
}

var numbers = [1,2,3,4,5,6,7,8,9];
var maxProduct = 0;

permute(numbers).forEach(function (permutation) {
    for (var i=1; i<9; i++) {
        var factor1 = parseInt(permutation.slice(0, i).join(""), 10);
        var factor2 = parseInt(permutation.slice(i, permutation.length).join(""), 10);
        var product = factor1 * factor2;
        if (product > maxProduct) {
            maxProduct = product;
            console.log("New maxProduct: " + maxProduct + " (factor1: " + factor1 + ", factor2: " + factor2 + ")");
        }
    }
});

Output:

...
  the last line follows:
  New maxProduct: 843973902 (factor1: 87531, factor2: 9642)