Hints from vague to increasingly specific:
Vaguest:
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×Since you've done the rest of this level, you have a good idea of how evil an architect mxvladi can be.
This means that a small detail which seems insignificant can actually be very important to clearing the room.
Less vague:
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×The upper-left tile is not the only tile where you can place a double.
Significant spoiler:
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×The clone potion is on grass.
If you need more after reading the above:
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×You need to clear the clone potion tile on the turn that you take it. This means pushing Beethro off, and also removing the weapon that pushes him off, as otherwise it will block the tile. You'll need the guard's help with that.