In building my table of 4s, I used some handsearching, and some computer tables. The tables created combinations of various 1 and 2four combinations, computing the values of each combo. I'm not going to share all of that code here (though it worked pretty well). Instead, here is the list of 'particles' that I used as input.


Manipulation of these particles generates lots of good solutions. A purely machinegenerated solution to the standard problem is probably not possible, as there are an infinite number of ways to manipulate each 4.