some calculations that might come in handy some time.

calculusCollection.js

/*
 Problem: how many collectible packets need to be bought to achieve a complete set, 
 when you don't know which one is in the packet.
 i.e. There are 16 unique trading cards to complete a set. Each is sold in a sealed enclosing.
 How many of them would it take to collect all 16?
 answer: about 54!
 https://plus.google.com/u/0/104223386721240823159/posts/goRYigJ4RGB
*/
var countCollectibles = function (collectibleCount) {
    var eulerConstant = 0.5772156649;
    return (collectibleCount * Math.log(collectibleCount) + eulerConstant * collectibleCount + 0.5);
}