There's a technique to making snakes go east without having to stand directly east of them. I'll try to explain the snake movement pattern to show why this technique works.
Snakes basically have a preference to either try and move horizontally towards you, or vertically towards you. This preference changes every 5 turns - horizontal, vertical, horizontal, etc. If they can't move the direction they would prefer to go to reach Beethro, they'll then try and move North, East, South and West, in that order.
Thus, if a snake is currently on vertical preference, and has just moved South, there will be a tail segment to the North of the head. If you then move North, the snake will try to move vertically to get to you, but it can't (because of its tail.) It will then try to move North (but can't), and then try to move East, and succeed.
Once that happens, you can then step behind the snake's head (to the west on the same horizontal row), where, due to another quirk, the snake will then go forward indefinitely. This works in any of the four cardinal directions.
These two techniques can come in handy in all sorts of snake rooms, even horde rooms where a bunch of snakes are just slapped down with no particular puzzle. But in this case, you can line up a snake head with a corridor on the east, and then send it in head-first, without having to stand inside the corridor yourself.
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