魔方陣ゲームの構築のための5次魔方陣の可能な場合数の算定高速化

概要

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Many kinds of magic squares have been employed so far for amusements We are planning to make one-person play-games of the 5×5 magic square programmed in a personal computer The game includes a subproblem how to calculate the number of feasible sets in a comparatively short time To begin with, constraints and pair-cell-exchanges of the 3×3 magic square are cleared up and the number of feasible sets is, in this case, only one And, in the same way, we checked the number in the 4×4 magic square to be 880 We proceed to the next study on the 5×5 magic square of 25 cells After considering constraints, number of independent variables results in 14 To shorten calculation time, we employ sum of squared number in all cells as a quadratic discriminant for pruning of implicit enumeration The number of sets is calculated to be 275,305,224 in 208 minutes by the personal computer with the CPU of Celeron 400 MHz
帝京平成大学の論文
2002-06-30