Setup and Rule Diagrams

[clem]

Can anyone help me figure out how to set up this game? I got all the questions eventually but it took me three times longer than it should’ve because I just could not figure out a good setup and had to keep going back to the rules. Any help would be mich appreciated!

[Daniel Stern]

Clem:

To set up this game, I'd first think about the concept of Numerical Distributions.

You have eight distinct elements, that you can list out: Rugs that have a material and a shape. I'd give them a letter for each. So my elements are:
OW
OW
RW
RW
RW
OS
RS
RS

And I can't repeat elements more than what I was initially told we have.

So I'm selecting between 4 and 6 out of eight. That's selecting at least half my elements every time, so I should have few enough being pushed "out" that I can track my out group also. Selecting between 4 and 6 sounds daunting at first, until you realize it is really only 3 options: pick 4, pick 5, and pick 6.

If I pick 4, 4 go "in" and 4 go "out."
If I pick 5, 5 go "in" and 3 go "out."
If I pick 6, 6 go "in" and 2 go "out."

So only 3 numerical distributions possible for my 8 elements. (I haven't yet decided how to diagram or visualize these distributions, just noting that 4-6 of 8 is a large selection and initially greatly limits what I can do with my elements)

First rule is okay, I've always gotta have 2 oval in my "in" group, got it.

Second rule should pop out at you as huge: I've been give five of my eight elements that are wool, but now I'm being told I can only pick 2 or 3 wool rugs. So picking only 2 or 3 out of 5 wool rugs will push several of the wool rugs to my "out" group each time.

I have two parts of this game -- limited numerical distributions by setup definition, and a rule severely limiting the number of my biggest element pool, the wool rugs -- that cause great limitations in how the game can be filled in. At this point, I'd consider templates:
let's try picking 6, the most rugs we can:
I want to use the fewest wool I can, 2, and try to pick 6. Can it be done? Nope! I only have 3 silk, or non-wool rugs. If I pick six carpets I have to use 3 wool

I might diagram my 6 rug template at this point: an in group of 6 elements(I did vertical lines for elements because order doesn't matter) and an out group of two. I'd write 3 W's in my in group, 3 S's in my in group, and 2 W's in my out group. Can I tell the shapes? well, to some extent. Since I have to use my oval silk, I need one oval wool to satisfy my "at least 2 oval" rule. My second wool will be rectangle. From those two sentences, I can fill in two of my W spaces with "OW" and "RW." Is my third wool rectangle or oval? Either, it turns out: no rule mandates what that third one will be, so I'd put a small O/R by my third W. My S's are all the S's, so that's easy: one OS, and two of RS.

My 5 rug template splits in two: Now I can do 5 with two wool or 3 wool. I'd make two templates for the 5-in in distribution, one with two wool and one with 3.

Same with 4 rug distribution: can be done with 2 wool and with 3 wool. Make 2 templates for the 4-in distribution.

For the shape/ material, you could track separately, stacked on top of one another like you learned in Advanced Linear Games Lesson. However, since I had listed all my elements out, I simply did an in group and out group, and put small slashes for alternate possibilities for a characteristic where I could not determine it with certainty.

I hope that is helpful.
Dan