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Gerrymandering Solution 5

detailed solution

In order for the no votes to win this election, we need to limit the yes votes to dominate just two districts. For this puzzle, let's instead focus on forming the three no-voting districts. With the wide selection of precinct voting patterns, what will it take to create a no-voting district? First, there are a few heavy no-voting precincts, highlighted below. Each one of these will form the core of the three no-voting districts.

Gerrymandering Detailed Solution Part 1

But the key to this puzzle are the precincts with 30 no votes and 20 yes votes, highlighted below. To form no-voting districts, we'll pair one 45 no / 5 yes with one 5 no / 45 yes (which cancel each other out) and we'll pair one 30 no / 20 yes with one 20 no / 30 yes (which again cancel each other out). Then we'll need one more 30 no / 20 yes precinct to create a no-voting district. There are six of these 30 no / 20 yes precincts, just enough to form three no-voting districts.

Gerrymandering Detailed Solution Part 2

Given the positions of these 30 no / 20 yes precincts, one no-voting district will have to pair the precinct in the lower right-hand corner and the precinct in the exact center of the puzzle. The others can be paired in one of two ways. The pairings on the left, however, cannot be connected to the 45 no / 5 yes precincts. This leaves the pairings on the right.

Gerrymandering Detailed Solution Part 3 Gerrymandering Detailed Solution Part 4

In order to construct the districts according to the plan laid out above, the no-voting districts along the left and top of the puzzle must be formed like this:

Gerrymandering Detailed Solution Part 5

Even though there are a couple of ways to form the last no-voting district, we also need to consider that the remaining two yes-voting districts must be formed with five precincts each. This leaves only one way to form the remaining districts.

Gerrymandering Detailed Solution Part 6