There are a lot of different ways to set this one up but mostly they rely on the same ideas Fogel posted above. Fogel's solution is really compact making it somewhat hard to see exactly what is going on. Here's a slightly more spread out version that hopefully shows off the ideas better so that you can see how one would reason out a solution.
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In both cases the construct starts by following the brain pathmap, which happens to path through the brain itself. Blocked by the brain, the construct if forced to make an alternate move that drops the trapdoor along that brain path map. The dropped trapdoor alters the brain path map, so that the new path map leads the construct back over the plate.
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Links to neat forum tools that I always have trouble finding:
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