Originally posted by brobluto
The board is infinite, so there is no "eventually".
Ah, that's what I missed, thank you. My method is the same as yours, only not that far away 🙂
I'm assuming the demon cannot see the angel during the first day, so he doesn't know where the angel starts out.
If the angel only moves horizontally or vertically;
The demon burns a square 3 paces away from the angel.
The next night, the demon can see in what direction the angel moved. The demon will try to make a square around the area the angel is in.
1) The angel moved towards the recently burned square.
Demon expands the wall on that side by burning a square above or below the existing wall. The demon must alternate between above and below.
2) The angel does not move towards the recently burned square.
Demon burns the square 3 paces ahead of the angel.
The third rule the demon must follow is when the angel moves north, he will expand the north side of the square by burning a square in front of the angel, in line with other burned squares already in the north wall of the square.
The fourth rule is that the demon will prevent the angel from moving in a space where a piece of wall would normally come. Rule 1 ensures that the angel will not escape by moving along a wall.
I hope that I made this clear. It works for me on paper.
For the angels that also moves diagonally:
I'm thinking that the same rules apply, but the demon needs to burn 4 paces away from the angel to determine the distance to the wall.