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- Conways_Soldiers abstract "Conway's Soldiers or the checker-jumping problem is a one-person mathematical game or puzzle devised and analyzed by mathematician John Horton Conway in 1961. A variant of peg solitaire, it takes place on an infinite checkerboard. The board is divided by a horizontal line that extends indefinitely. Above the line are empty cells and below the line are an arbitrary number of game pieces, or \"soldiers\". As in peg solitaire, a move consists of one soldier jumping over an adjacent soldier into an empty cell, vertically or horizontally (but not diagonally), and removing the soldier which was jumped over. The goal of the puzzle is to place a soldier as far above the horizontal line as possible.Arrangements of Conway's soldiers to reach rows 1, 2, 3 and 4. The men marked \"B\" represent an alternative to those marked \"A\".Conway proved that, regardless of the strategy used, there is no finite series of moves that will allow a soldier to advance more than four rows above the horizontal line. His argument uses a carefully chosen weighting of cells (involving the golden ratio), and he proved that the total weight can only decrease or remain constant. This argument has been reproduced in a number of popular math books.Simon Tatham and Gareth Taylor have shown that the fifth row can be reached via an infinite series of moves [1]; this result is also in a paper by Pieter Blue and Stephen Hartke [2]. If diagonal jumps are allowed, the 8th row can be reached but not the 9th row. It has also been shown that, in the n-dimensional version of the game, the highest row that can be reached is 3n-2. Conway's weighting argument demonstrates that the row 3n-1 cannot be reached. It is considerably harder to show that row 3n-2 can be reached (see the paper by Eriksson and Lindstrom).".
- Conways_Soldiers thumbnail Conways_soldiers.svg?width=300.
- Conways_Soldiers wikiPageExternalLink mathproblems.info.
- Conways_Soldiers wikiPageExternalLink xfile.
- Conways_Soldiers wikiPageExternalLink solarmy.pdf.
- Conways_Soldiers wikiPageExternalLink solarmy.
- Conways_Soldiers wikiPageExternalLink checker.shtml.
- Conways_Soldiers wikiPageExternalLink index.html.
- Conways_Soldiers wikiPageExternalLink www.integers-ejcnt.org.
- Conways_Soldiers wikiPageExternalLink ~shartke2.
- Conways_Soldiers wikiPageID "2017897".
- Conways_Soldiers wikiPageID "28051729".
- Conways_Soldiers wikiPageLength "54".
- Conways_Soldiers wikiPageLength "8113".
- Conways_Soldiers wikiPageOutDegree "1".
- Conways_Soldiers wikiPageOutDegree "11".
- Conways_Soldiers wikiPageRedirects Conways_Soldiers.
- Conways_Soldiers wikiPageRevisionID "409857848".
- Conways_Soldiers wikiPageRevisionID "690216082".
- Conways_Soldiers wikiPageWikiLink Category:Mathematical_games.
- Conways_Soldiers wikiPageWikiLink Category:Single-player_games.
- Conways_Soldiers wikiPageWikiLink Conways_Soldiers.
- Conways_Soldiers wikiPageWikiLink Dimension.
- Conways_Soldiers wikiPageWikiLink Golden_ratio.
- Conways_Soldiers wikiPageWikiLink Infinity.
- Conways_Soldiers wikiPageWikiLink John_Horton_Conway.
- Conways_Soldiers wikiPageWikiLink Mathematical_game.
- Conways_Soldiers wikiPageWikiLink Peg_solitaire.
- Conways_Soldiers wikiPageWikiLink Simon_Tatham.
- Conways_Soldiers wikiPageWikiLink Taxicab_geometry.
- Conways_Soldiers wikiPageWikiLink File:Conways_soldiers.svg.
- Conways_Soldiers wikiPageWikiLinkText "Conway's Soldiers".
- Conways_Soldiers title "Conway's Soldiers".
- Conways_Soldiers urlname "ConwaysSoldiers".
- Conways_Soldiers wikiPageUsesTemplate Template:MathWorld.
- Conways_Soldiers wikiPageUsesTemplate Template:R_from_modification.
- Conways_Soldiers subject Category:Mathematical_games.
- Conways_Soldiers subject Category:Single-player_games.
- Conways_Soldiers hypernym Game.
- Conways_Soldiers type VideoGame.
- Conways_Soldiers type Redirect.
- Conways_Soldiers comment "Conway's Soldiers or the checker-jumping problem is a one-person mathematical game or puzzle devised and analyzed by mathematician John Horton Conway in 1961. A variant of peg solitaire, it takes place on an infinite checkerboard. The board is divided by a horizontal line that extends indefinitely. Above the line are empty cells and below the line are an arbitrary number of game pieces, or \"soldiers\".".
- Conways_Soldiers label "Conway's Soldiers".
- Conways_Soldiers label "Conways Soldiers".
- Conways_Soldiers sameAs Q5015732.
- Conways_Soldiers sameAs Conwayovi_vojáci.
- Conways_Soldiers sameAs Soldados_de_Conway.
- Conways_Soldiers sameAs חיילי_קונוויי.
- Conways_Soldiers sameAs m.06ffd4.
- Conways_Soldiers sameAs Q5015732.
- Conways_Soldiers wasDerivedFrom Conways_Soldiers?oldid=409857848.
- Conways_Soldiers wasDerivedFrom Conways_Soldiers?oldid=690216082.
- Conways_Soldiers depiction Conways_soldiers.svg.
- Conways_Soldiers isPrimaryTopicOf Conways_Soldiers.