This 3D-version of Connect Four is named Sogo in (continental?) Europe, for example: http://fr.wikipedia.org/wiki/Sogo (France) http://de.wikipedia.org/wiki/Sogo (Deutschland) I can see 16 preferential places where it is interesting to play, on the 64 positions: -the 8 corners of the 4x4x4 cube -the 8 places of the central 2x2x2 cube
From each of these 16 places, there are 7 possible alignments. The 64 - 16 = 48 other places offer only 3 or 4 possible alignments.
About Connect Four, there are versions for one player: Morpion Solitaire 4T and 4D. www.morpionsolitaire.com Fully solved by Michael Quist in 2008, with a maximum of 62 and 35 moves, respectively. Christian. -----Message d'origine----- De : math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] De la part de Allan Wechsler Envoyé : mercredi 1 février 2012 21:42 À : math-fun Objet : [math-fun] Score Four Wikipedia says that Connect Four was shown to be a first-player win in 1988, but doesn't mention any similar analysis of the structurally similar game Score Four. It also feels like a first-player win to me, and I wonder if anybody knows anything about it for certain. Score Four is played on a square 4x4 array of posts; each post is tall enough to accommodate 4 playing beads. The board starts empty. Two players take turns; on your turn you slide a bead of your assigned color onto a post of your choosing; you can't choose a post that already has four beads on it. The bead will slide down to the lowest unoccupied place on the post. The object of the game is to establish a line of four beads of your color. This line may be horizontal, vertical, or diagonal; the winning lines are exactly the same as in Qubic. Score Four may be regarded as Qubic with the extra rule that one is required to play in the lowest unoccupied cell of a given column. Good players establish "traps", incomplete lines of three out of four beads, where the missing cell of the line has one void below it. The opponent can't play on that post without enabling the placement of the missing bead. In the endgame, the players alternate playing on un-booby-trapped posts until they run out of room; the player who plays on a booby-trapped post first loses. Surely if the exercise hasn't been done yet, this game would succumb to mere minutes of computer analysis. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun