One of my science students, PK, recommended a game to me called Doodle God, from JoyBits Ltd. My student said, “since we are studying chemistry, which is about combining things, check out this game, where you try to combine things.”
I was excited to give it a try and have now been playing it off-and-on for about a month.
Here’s what I like
- Easy to learn to play.
- Very rewarding to see two things swirl and create something new.
- Some combinations are very creative, not immediately obvious, but logical.
Here’s what I don’t like
- From the start, the portrayal of a monotheistic, creative deity as a grandfatherly, tinkering, bumbling, bug-eyed, wild-haired, white-bearded, tongue-protruding simpleton, seems borderline blasphemous for at least three major religious traditions of the world. But, hey, whatever sells…
- When I let my 8-year-old play—ignoring the 13+ rating of the game—I should not have been too surprised when certain risqué themes emerged. Alcohol, drugs, sex, [censored], rock-n-roll are all there, and were they all necessary? But, hey, whatever sells…
- From the beginning I was a little peeved when I tried to combine certain things—that made logical sense to me—but they didn’t combine. Similarly, when I saw hints which led to things that did wondrously(?) and improbably combine, I almost put the game down. (And how was I supposed to guess that?)
Seeing that the dislikes for me seem to outweigh the likes, why am I writing this blog post? I feel this game is *so close* to being something of real and amazing educational value. Imagine something like “Chemistry Zeus” [any similarities between deities living or dead is purely coincidental], where students start with a few elements and either bombard them to make new elements (nuclear physics) or combine them with other elements or molecules to make compounds, or whole families of substances. I think I would play that game, and if it taught a little science or history of science along the way, cool!
JoyBits, if you need a scientific consultant, you can contact me.
Some math fooling around
You start with 4 elements and are asked to deduce pairings that create successively more complex elements. Since the deduction part is flawed in my opinion, I believe most successful game-players resort to trial and error. Let me explain.
If I give you N items and tell you some of them might pair, by trial and error you would take the 1st item and try to pair it with the 2nd, 3rd, 4th, etc. up to N. When you are done with the 1st item you then take up the 2nd item, and try some pairings, but you don’t have to test it with the 1st item, since you already did that, so you test 2nd+3rd, and 2nd+4th, and 2nd+5th, etc. one way to visualize this is with a grid.
1 | 2 | 3 | |
1 | 1+1 | 1+2 | 1+3 |
2 | X | 2+2 | 2+3 |
3 | X | X | 3+3 |
The square with 1+1 means you are taking the 1st element in the game and trying to pair it with itself. The 1+2 means that you are trying to pair the 1st element with the 2nd element. Notice that the square that would be 2+1 in this example is marked with “X”. That means you don’t need to test that combination because in the game 1+2 is the same as 2+1, the order you click on elements to pair them in the game doesn’t matter. (If someday it did, the following analysis would be invalid.)
The formula for how many pairings you have to check for N total elements is
Total Pairs You Need to Check = N2-(1/2)(N-1)(N)
(thanks to Wolfram Alpha for helping me evaluate a sum)
We can verify that this formula is correct, by checking for N=3, plugging that into the formula and then counting in the table above to see if the results agree. For N=3, from the table I would need to check 6 pairings to exhaust all possible combinations in the game. The formula predicts
Total Pairs You Need to Check = N2-(1/2)(N-1)(N)
Total Pairs You Need to Check = 3*3-(1/2)(3-1)(3)=9-(1/2)(2)(3)=9-(1/2)(6)=9-3=6.
Now, the object of the game is to find successful pairings so let’s say 1+1 is successful. But that would produce a 4th element. That means we have to check more potential pairs. (Note that some pairings produce two elements, that happens pretty rarely so the analysis so far and following is not invalidated.)
If successful, then you create a 4th element, and the table would now look like this:
1 | 2 | 3 | 4 | |
1 | 1+1 | |||
2 | N | |||
3 | N | N | ||
4 | N | N | N |
N = total number of elements in the game that you start with.t = the turn of the game that you are on, in other words how many pairs you have tried alreadys = successful matches alreadyu = unsuccessful matches already
t = s + u
Potential Matches Left = (N+s)2-(1/2)(N+s-1)(N+s)-tIn the example above, N=3, t=1, s=1, u=0, the number of matches left to test, i.e. the number of blank squares in that grid is:(3+1)2-(1/2)(3+1-1)(3+1)-1=16-(1/2)(3)(4)-1=16-(1/2)(12)-1=16-6-1=9.