dc.contributor.author Gács, Peter en_US dc.date.accessioned 2018-06-13T15:51:32Z dc.date.available 2018-06-13T15:51:32Z dc.date.issued 2007 dc.identifier.citation P Gács. 2007. "The angel wins." arXiv preprint arXiv:0706.2817, dc.identifier.uri https://hdl.handle.net/2144/29379 dc.description.abstract The angel-devil game is played on an infinite two-dimensional “chessboard” Z2. The en_US squares of the board are all white at the beginning. The players called angel and devil take turns in their steps. When it is the devil’s turn, he can turn a square black. The angel always stays on a white square, and when it is her turn she can fly at a distance of at most J steps (each of which can be horizontal or vertical) steps to a new white square. Here J is a constant. The devil wins if the angel does not find any more white squares to land on. The result of the paper is that if J is sufficiently large then the angel has a strategy such that the devil will never capture her. This deceptively easy-sounding result has been a conjecture, surprisingly, for about thirty years. Several other independent solutions have appeared also in this summer: see the Wikipedia. Some of them prove the result for an angel that can make up to two steps (including diagonal ones). The solution opens the possibility to solve a number of related problems and to introduce new, adversarial concepts of connectivity. dc.relation.ispartof arXiv preprint arXiv:0706.2817 dc.subject Combinatorics en_US dc.subject Mathematics en_US dc.subject Computer games en_US dc.title The angel wins en_US dc.type Article en_US pubs.elements-source manual-entry en_US pubs.notes Embargo: No embargo en_US pubs.organisational-group Boston University en_US pubs.organisational-group Boston University, College of Arts & Sciences en_US pubs.organisational-group Boston University, College of Arts & Sciences, Department of Computer Science en_US
﻿