Angel vs Demon

no the angel will win just keep moving in one direction and thats it

The angel cannot move forward if he has a burned square in his path. The new version has him making two individual moves, but neither one can land him in a burned area.

I suspect that regardless of how many consecutive orthogonal move an angel can make, that the devil can eventually trap him, although it requires more pre-planning and a greater distance the angel can travel.

I do not, however, have proof of this, and I haven't yet derived a potential solution.

I'm fairly sure that if the angel can move three times each day it can escape.

well think of it if the Angel moves lets just say only north then how can the Demon cant him if he is behind the Angel??

Originally posted by O Artem O
well think of it if the Angel moves lets just say only north then how can the Demon cant him if he is behind the Angel??

"At midnight each day, the demon burns any square on the chess board, except it can't burn the square the angel is currently on"

yea sooo, the board is infinite just move in the opposite direction

Originally posted by O Artem O
yea sooo, the board is infinite just move in the opposite direction

Then the demon will burn the board in that direction. The demon doesn't have to "catch up" with the angel.

Originally posted by O Artem O
yea sooo, the board is infinite just move in the opposite direction

OK
I challenge you on a 9x9 board
You are Angel at E5.
What is your move?

the board is infinite has no dimensions

Originally posted by O Artem O
the board is infinite has no dimensions

OK the borad is infinite.
Start on E5 for simplicity.
I will catch you before you get out of the 9x9 square

btw: its infinite but still only 2 dimensions ... no hyper-space jumps! 😉

Originally posted by brobluto
I think 10 spaces for 4-direction and 40 spaces for diagonal work. They may not be the most efficient, but it get's the job done.

I still don't see how the diagonal is possible.

Originally posted by Palynka
I still don't see how the diagonal is possible.

If angel moves to (1,1), burn (40,40). angel moves to (2,2), burn (40,39), angel moves to (3,3), burn (39,40) etc

What are the minimum number of moves for the devil to catch a single-space-diagonal-allowed (SSDA) Angel? Assume of course that the Angel is not helping.

For that matter, what are the minimum moves where the Devil "mates" the Angel, where the Angel helps (but won't make an accidental step onto a burnt square)?

Can the Devil still catch the Angel if the Angel can repair one square every five turns? Every two turns?

Originally posted by Gastel
Can the Devil still catch the Angel if the Angel can repair one square every five turns? Every two turns?

And what if the Angel can move 3 suares on every prime number move?




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