Ok, I am stuck here.
I can kill one of the mothers, but then I can try two things, neither of which work.
1.
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×I can wipe out all the tar on that side (while leaving a plug of tar at the entrance), but once I open the entrance I am overrun with roaches (as I cannot get to a safe place).
2.
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×I can clear most of the tar, but leave a safe spot where I can slaughter roaches. In this case, by the time the roaches are gone, the tar has grown to almost fill the room again. Then I can:
a) Go kill the tar again, leaving me back where I started.
or b) Leave at kill roach queens and have the tar grow to an uncutable mass behind me.
Either way, the best I can do is to maintain a steady state.
I am obviously missing something, but I don't know what...