Math Skills Game Advice
Assumptions I made:


The 3 object will have 3 arrays, just as the 67 object will have 67 arrays
The "combined" array can be computed on demand
Each call to pickNumbers for a certain object will always have the same parameters


Firstly for your objects, I think they belong in a namespace and also a way to define which numbers you want to be in the game:

var Game = {}
Game.NUMBERS = [3, 5];


Next instantiate all the classes:

for (var i = Game.NUMBERS.length; i --) {
  Game[Game.NUMBERS[i]] = new GameNumber(Game.NUMBERS[i]);
}


Let's define what your class would look like:

var GameNumber = function(number) {
  this.number = number;
  this.arrays = [];
  for (var i = number; i --) {
    this.arrays.push([])
  }
}
GameNumber.prototype.combined = function() {
  Array.prototype.concat.apply([], this.arrays)
}
GameNumber.prototype.pick = function(arrayLength, sum, max, min) {
  for (var i = this.number; i --) {
    pickNumbers(this.arrays[i], arrayLength, sum, max, min);
  }
}


Cool, so now you can create your objects in a sufficiently general way and call pick or combined on any of them.

Game[3].pick(5, 40, 20, 1);
Game[3].combined() // Output: [...]


As for the pickNumbers function, I didn't look at the logic too heavily, I'm sure that's working how you want it to. The variable names I would simplify to array, arrayLength, sum, max, min for readability. You may also want to attach it to the Game object so you have less globals (ie Game.pickNumbers = function(...)). I'd also try and abstract the html from it so as to separate logic from presentation.

Note: I haven't tested this code, it's only to give you an idea of how to structure it.