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[_r.u.s.s.]

even though i predict this thread to fail because of lack of interest, i will post it anyways

imagine an infinite chess board. on this board there is a chess piece- Angel, which can move in any direction, in distance of maximally n squares per one turn

the second player is Devil, which can remove any chessboard square per turn, creating a hole, so angel won't be able to step on it. angel is able to leap over holes but can not stand on them

*devil wins if he traps angel inside of an island surrounded by a hole of length n, so angel can't leap over the hole and escape from this island.

*angel wins if he's able to move infinitely without getting trapped


questions are:
can angel win? can devil win?
can angel always win?
can angel win if his [n] power is high enough?
can devil trap angel of any finite power? (be aware that this is an infinite chess board and the board pieces destroyed by devil may be light years far away)

discuss! (try thinking before using google )

[SlowCoder]

1. You don't say how many other board pieces there are.
2. You don't specify how the Devil can move; distance, direction, etc.; only that the Devil can remove any piece it wants.

Is there anything saying the Devil can't remove the Angel piece, winning instantly?

[_r.u.s.s.]

read again carefuly, the chessboard is infinite

there is only angel chesspiece

devil doesn't move, he's not on chessboard and removes pieces of "ground". he doesn't remove the chesspieces! he can't remove angel (he is only one on the board), he removes the sqares of chessboard grind, where angel could step, leaving a hole, so angel won't be able to step on it. how else can i explain it?

[dosraider]

Maybe *maybe* it would be more interesting to discuss this fine specimen of the human race, more specific his brain, or lack of.

[Lulu_Jane]

Unless the angel is stupid, can't it go on forever?

[Eagle of Fire]

Angel cannot win unless you can define infinity.

Angel lose.

End of story.

[arete]

Mmm, chessboard of infinite size? If length of side is n, then n is infinity, yes? But, the number of squares on the board is also infinite, as is the surface area of the board, n x n. What you're essentially saying is there would only be one square left, for the piece A to stand on: Therefore d must be able to remove n-1 squares from the board, in order to win. This is a paradox, because if that's possible, infinity - n - must be quantifiable. Because otherwise there will always be more squares for A to move to. Infinity minus one is still infinity. If you can count them, however, it's not infinity. The board is huge, of course, but not infinite. It can be argued that the universe itself is not infinite, so now we're talking quantum? In which case, I'd rather talk about something else.

[The Fifth Horseman]

If the devil focuses on building a large "moat" of pits and then takes out the borders of the large "island" formed that way before the angel can run out... yeah, he can win.

[arete]

Was I wrong in understanding that angel can jump over any number of empty spaces?

[The Fifth Horseman]

The angel's [N] can be anything from 1 to infinity. For angels with low [N], it's definitely possible to trap them.