Ok, progressive hints.
×When the snake is below the hole, you have to be directly in front of it, or directly behind it. Otherwise it will always get stuck. (It's on a 20-move cycle, so every time it gets there it prefers vertical movement.)
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×So, you have to keep waiting till it's just past the hole, dive down, get a trapdoor or two, and make it back up in time.
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×You can't get the bottom trap and make it back up in time, so drop it last.
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×It's ok if the snake gets a little shorter, so don't worry if you can't get the last trap quite in time.
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×A few tips:
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×Start with the traps at the bottom and work your way up.
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×Don't necessarily grab every trap you can on your way up. It may pay to leave one or two you could just as well drop, so they don't get in the way. Balance that against time. You have to hurry.