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[Mighty Midget]

It doesn't matter if the square removed is just next to Angel or lightyears away. The main point is that from Angel's point of view, that removed square puts a limit in only one of 8 directions, at the most. With only one square removed, a maximum of one direction is closed, leaving Angel to choose from any of the other 7. If we ignore any diagonals and just look at the horizontal/vertical movements, that still leaves three movements.
All Angel has to do to make sure Devil never traps him/her/it, is to always move in one of two directions say, down and left, and never up and right. That will always give Angel an escape route.

[Japo]

Originally Posted by _r.u.s.s.

you're making no sence, that's actually why the devil could trap the angel of any power, if it's true

No, even if you were interested in the limit where the size of the trap tends to infinity, the distance the angel can travel before it's finished would diverge faster, for any N>0.

A strong and definitive way of proving that the devil can trap an angel (without necessarily proving that it's the max powered angel he can trap?) would be proving that he's able to build a moat around a trap larger than the area the angel can reach in the time the trap takes to be built. But as I said that's not even true for the minimal N=1.

Any other strategy for trying to prove anything doesn't seem robust, since it needs a hypothesis in the form of the strategy the angel is going to follow consistenly and blindly (even for a obviously contraproductive move). First you'd have to prove that it's the optimal strategy in any circumstance, and that looks more difficult to prove, if possible at all, which I doubt. At least all the demonstrations in the article are that way.

[sgtboat]

Ya'll are making my head hurt.

[AlumiuN]

Japofran is right, how can we prove that two players with human-based intelligence can block one another at any given time? We can't.

[_r.u.s.s.]

Originally Posted by Japofran

No, even if you were interested in the limit where the size of the trap tends to infinity, the distance the angel can travel before it's finished would diverge faster, for any N>0.

you didn't get me, i meant to say that infinitely large board allows devil to build moat at any distance, so n can raise into huuuge numbers

[arete]

I think it's safe to guess which field Japo is in IRL... LOL

[Kugerfang]

Both can win or lose.

[Japo]

Originally Posted by arete

I think it's safe to guess which field Japo is in IRL... LOL

The Devil hasn't got me yet IRL.

[AlumiuN]

Originally Posted by Japofran

The Devil hasn't got me yet IRL.

With the conditions in _r.u.s.s's 'riddle', he won't. Not unless you make a mistake... :trip:

[_r.u.s.s.]

how can you be sure about it, prove it=P