Okay, so I feel a little silly, except what I was doing was actually productive.
×So I hadn't thought of luring the adder to the west wall to force it into the bottom row.
At its full length, the adder dies in the exact number of turns it takes for the briar to grow to the pressure plate, and your sword is forced to the right so you can't wait until one turn before and make the final stab yourself.
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×However, my misguided attempts to lead the adder in from the northeast section of the room were quite good at shortening it.