OK, I can see how CSR's method would work, but I have a (99%) exhaustive proof that the other way isn't possible. Can someone please point out the 1% mistake in the following?
×
There is no way to get the mimic from its chamber to the mud blob in the top left of the entire room, so we assume that is already destroyed.
There are 6 places the mimic could be when it destroys the last 2x2 mud blob.
Firstly, the last blob to be destroyed cannot be the top or right 2x2 blob. There are only two places where Beethro can move southwest or southeast and not have the mimic move down; the very bottom of the mimic's chamber or when the mimic is at 2/3. Even if after doing so Beethro is at the very bottom of his chamber, the mimic still needs to go up at least two squares, making Beethro north of the black sister gate.
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Suppose mimic is at 1.
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×There will be babies at 6,9,10, and also 13 since there's no way to get a sword there earlier.
Move southeast; mimic is blocked by baby at 6 and moves to 5. Still babies at 6,10,13.
Move south; mimic moves to 9. Babies at 5,10,13.
Move north or southeast; mimic is blocked and dies.
Suppose mimic is at 6.
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×Then babies would have been just created at 11/13/14.
Move southeast. Baby at 11 blocks mimic, mimic moves to 10.
Move south. Mimic moves to 13; baby moves from 11 to 10.
Mimic is now blocked and will die next turn whether we move north or southeast.
Suppose mimic is at 7, and there is a baby at 12.
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×Move southeast. Baby at 12 blocks mimic, mimic moves to 11.
Move south. Mimic moves to 14, baby moves to 15.
Move north/south as many times as you please; still end with mimic on 14, baby on 15.
Move southeast. Mimic dies due to baby at 15.
Suppose mimic is at 7 and there isn't a baby at 12.
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×Move southeast. Mimic moves to 12.
Move south. Mimic moves to 15.
Move north/south as many times as you please. Mimic still at 15.
Move southeast. Mimic dies.
Suppose mimic is at 4 and there is no baby to its southeast.
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×Mimic will hit rotator.
Suppose mimic is at 4 and there is a baby to its southeast.
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×Move southeast. Mimic moves to 8.
Move south. Mimic moves to 12.
Move north/south as many times as you like. If mimic was blocked to the north it go to 15 then die, otherwise it will still end up at 12.
Move southeast. Mimic will move to 15.
The mimic cannot move southeast or it will die. If there is a baby at 11, then after any combination of northwest/north/south/southeast, mimic will return to 15.
There is a possibility things could change if the mimic moves northwest to 11, and a baby moves to 15. Now moving southeast takes the mimic to 14. We then have to repeat this process again to get another step left.
However, I've tried all possibilities for which babies to leave alive in that last case (and there aren't really many, since you must use the lower mud blob to push Beethro a square lower), and it simply isn't possible.