# Factorial Games

By Deane Barker on March 15, 2006

There are a couple interesting Flash games I’ve seen lately that both subscribe to a particular format: pick choices in the right order.

It started with Grow, and its siblings Grow RPG and Grow Cube (all found from this list). I liked Grow Cube the most of all. You pick…things — fire, a bowl, a spring, etc. — and the cube uses them to evolve. You have to pick them in the right order for your cube to reach its maximum potential.

It sounds simplistic, and it is. But it’s also fascinating to rearrange the order in which you pick some things and suddenly have your cube thrive in a new way. I cheated and found a solution, and the ultimate evolution of the cube was magnificent.

Now I see Cityscape which is along the same lines — call it miniature SimCity. You pick from a menu of 20 industries and improvements for your city (Mining, Fishing, Media, Police, etc.), and the order in which you pick them makes a difference on how well your city does. Picking X at any point may only do its best if you’ve already picked Y and Z earlier. Option A’s results may be stunted if B is already implemented, etc.

My best in Cityscape is 36 out of 60. I keep sending in the Explorers first, then adding Mining, then Surveyors. I suspect this isn’t optimal, but I can’t seem to break out of the rut.

The mathematical principle behind this format is the factorial, expressed as n!. What it means is that the total number of choices is n * (n-1) * (n-2) and down to zero. The logic says that you have 20 choices to start out with. You pick one, and then you have 19. You pick another one, and then you have 18. And so on.

So with 20 choices, there are 2,432,902,008,176,640,000 possible ways we can put them in order. Only one of 20 ways is the right one, though the order can be derived through logic and skill, so it’s not completely random. Even the original Grow, with just 12 choices, results in 479,001,600 possible combinations. (Here’s a factorial calculator, if you’re interested.)

Has anyone else seen other examples of these type of games?

So what is the right order for the Grow Cube? It’s been an addiction since I saw this post and I would really love to know the sequence to get the ultimate result. Any hints????

Google for “grow cube solution”. It’s the first result.