You have to kill that original roach, so that's one, leaving 22 more to kill. Time for some math.
You can generate 4 roaches every spawn right?...
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×or you could generate 3 if you stand on one of the corners (say at (19,17) on turn 30.
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×If you spawn and kill 4 roaches the first 3 turns, then stand in one of the corners and spawn and kill just 3 roaches the next three turns, that's 21. Killing the queen gets you to 22 (plus that first roach you killed will make 23). So you should be perfect.
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Links to neat forum tools that I always have trouble finding:
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