@GeePawHill or go even smaller, a 2x2 with 3-ominos and walk the algorithm by hand.
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How important is gerrymandering? Very very important.
Spoze your state has 5 congressfolk. Spoze there are 16 million orange voters and 9 million purple voters. You might expect to return 3 orange & 2 purple congressfolk.
But if the districts are drawn carefully, gerrymandering can return *1* orange and *4* purple congressfolk.
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And, so you're clear on this, it can go the other way, too. With careful drawing of the map, you can return *5* orange and *0* purple congressfolk. That's *also* gerrymandering.
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Inching towards the geekery part here.
I wanted to make a puzzle game based on these ideas, hoping to educate folks about how it works, as well as give them fun puzzles to solve.
I'd give, let's take our 5x5 16-orange 9-purple all laid out on a grid, and challenge you to draw the districts, one for the 1-4, and one for the 5-0.
That was in 2020, and I totally lost that thread, tho I had fun working on it. You know how side projects are.
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Having a known puzzle and presenting it to the user, child's play, right? Any of us who has UI chops could roll that.
But I didn't want to *curate* these puzzles. I wanted to *generate* them.
User specifies grid. App decides on the orange-purple ratio, and lays out which squares are which. User solves it.
Sit back and wait for the stock options to mature, innit.
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But wait. You can't just randomly distribute 16-9 into a 5x5 grid. That may or may not be gerrymanderable to create 5-0 or 1-4 voting.
The generated puzzle *must* be solvable.
How the *fuck* are we gonna be sure of that?
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After miles of pacing around out on the deck, hundreds of cigarettes, and a certain amount of substance abuse, I figured it out:
If I could tile the grid with polyominos -- districts -- they would be a solution to the puzzle, cuz I could, for each polyomino, put the correct ratio of orange to purple to achieve the desired outcome.
It wouldn't be the *only* possible solution, but it would be one *guaranteed* solution.
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