Pushing the queen towards the corner is all about timing Beethro's movements. Let's start with the queen alternating between (18,12) and (19,11) -- this is easy to reach, although let me know if you need help getting there.
×Why does the queen move SW from (19,11)? She imagines what a brained roach would do. There are multiple paths to Beethro of the same length, and the roach would prefer E over S because of directional preferences (N, W, E, S, wait, then diagonal directions). So the queen prefers W and corrects this to a diagonal move.
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×To make the queen move west from (19,11), the roach's first choice must be south, i.e. the path starting with a south move must be strictly shorter.
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×Okay, but now the queen is alternating between (18,11) and (19,11). To get her to move W or SW from (18,11), the brained roach move must be east, so we need to find a spot close to the boundary of (roach prefers south) and (roach prefers east) where we can easily switch from one to the other.
