04.05.2020, 22:50
Zunächst mal nur das 9-Damen-Problem ohne die 3x3-Blöcke des Sudoku:
Es gibt 352 Möglichkeiten, 9 Damen auf einem 9x9-Brett aufzustellen, so dass sie einander nicht bedrohen.
Es gibt 1552 Möglichkeiten, sieben disjunkte Lösungen auszuwählen. Es ist nicht möglich, acht oder neun disjunkte Lösungen auszuwählen.
Mit der zusätzlichen Sudoku-Bedingung (in jedem 3x3-Block steht genau eine Dame) verbleiben noch 144 von 352 Lösungen, und es gibt nur noch 24 Möglichkeiten, sieben disjunkte Lösungen auszuwählen:
[0, 4, 6, 8, 3, 1, 7, 5, 2]/[1, 8, 5, 2, 4, 7, 0, 3, 6]/[2, 5, 7, 4, 0, 8, 6, 1, 3]/[3, 0, 8, 5, 2, 6, 1, 7, 4]/[4, 7, 0, 3, 6, 2, 5, 8, 1]/[6, 3, 1, 7, 5, 0, 2, 4, 8]/[7, 2, 4, 1, 8, 5, 3, 6, 0]/
[0, 4, 6, 8, 3, 1, 7, 5, 2]/[2, 5, 8, 1, 4, 6, 3, 0, 7]/[4, 1, 7, 2, 6, 3, 0, 8, 5]/[5, 7, 2, 0, 8, 4, 1, 3, 6]/[6, 3, 1, 7, 5, 0, 2, 4, 8]/[7, 0, 3, 6, 2, 5, 8, 1, 4]/[8, 2, 5, 3, 0, 7, 4, 6, 1]/
[0, 4, 6, 8, 3, 1, 7, 5, 2]/[2, 6, 3, 1, 8, 4, 0, 7, 5]/[3, 1, 8, 4, 0, 7, 5, 2, 6]/[4, 2, 7, 5, 1, 8, 6, 0, 3]/[5, 8, 2, 0, 7, 3, 1, 6, 4]/[6, 3, 1, 7, 5, 0, 2, 4, 8]/[7, 5, 0, 2, 4, 6, 8, 3, 1]/
[0, 5, 7, 2, 6, 3, 1, 8, 4]/[2, 8, 5, 1, 4, 6, 0, 3, 7]/[3, 6, 2, 7, 1, 4, 8, 5, 0]/[4, 1, 8, 0, 5, 7, 2, 6, 3]/[6, 0, 3, 5, 8, 2, 4, 7, 1]/[7, 2, 4, 8, 0, 5, 3, 1, 6]/[8, 3, 0, 4, 7, 1, 6, 2, 5]/
[0, 5, 8, 4, 1, 7, 2, 6, 3]/[1, 6, 4, 0, 8, 3, 5, 7, 2]/[2, 8, 5, 3, 0, 6, 4, 1, 7]/[4, 7, 0, 8, 3, 1, 6, 2, 5]/[5, 2, 6, 1, 7, 4, 0, 3, 8]/[6, 0, 3, 7, 4, 2, 8, 5, 1]/[8, 3, 1, 6, 2, 5, 7, 0, 4]/
[0, 5, 8, 4, 1, 7, 2, 6, 3]/[1, 7, 4, 2, 8, 5, 3, 0, 6]/[3, 6, 2, 7, 5, 0, 8, 1, 4]/[4, 8, 1, 3, 6, 2, 7, 5, 0]/[5, 2, 6, 1, 7, 4, 0, 3, 8]/[6, 1, 3, 5, 0, 8, 4, 2, 7]/[7, 3, 0, 6, 4, 1, 5, 8, 2]/
[0, 5, 8, 4, 1, 7, 2, 6, 3]/[2, 8, 3, 7, 4, 1, 5, 0, 6]/[3, 6, 2, 5, 8, 0, 7, 4, 1]/[4, 1, 7, 0, 3, 6, 8, 5, 2]/[5, 2, 6, 1, 7, 4, 0, 3, 8]/[6, 3, 0, 2, 5, 8, 1, 7, 4]/[7, 4, 1, 8, 0, 3, 6, 2, 5]/
[0, 6, 3, 5, 8, 1, 4, 2, 7]/[1, 8, 5, 2, 6, 3, 0, 7, 4]/[2, 5, 7, 1, 3, 8, 6, 4, 0]/[3, 1, 6, 8, 0, 4, 7, 5, 2]/[4, 7, 1, 6, 2, 5, 8, 0, 3]/[6, 3, 0, 7, 4, 2, 5, 8, 1]/[8, 4, 2, 0, 5, 7, 1, 3, 6]/
[0, 6, 3, 7, 2, 4, 8, 1, 5]/[1, 4, 7, 0, 8, 5, 2, 6, 3]/[2, 5, 8, 6, 1, 3, 7, 0, 4]/[3, 7, 0, 4, 6, 1, 5, 2, 8]/[4, 8, 1, 5, 7, 2, 0, 3, 6]/[5, 2, 6, 3, 0, 8, 1, 4, 7]/[6, 0, 5, 1, 4, 7, 3, 8, 2]/
[0, 6, 3, 7, 2, 4, 8, 1, 5]/[1, 4, 7, 0, 8, 5, 2, 6, 3]/[2, 8, 5, 1, 4, 6, 0, 3, 7]/[3, 7, 0, 4, 6, 1, 5, 2, 8]/[5, 2, 8, 3, 0, 7, 1, 4, 6]/[6, 3, 1, 8, 5, 2, 4, 7, 0]/[8, 1, 4, 6, 3, 0, 7, 5, 2]/
[0, 6, 3, 7, 2, 4, 8, 1, 5]/[1, 5, 8, 2, 4, 7, 3, 0, 6]/[2, 4, 7, 1, 8, 5, 0, 6, 3]/[3, 7, 0, 4, 6, 1, 5, 2, 8]/[5, 2, 6, 3, 0, 8, 1, 4, 7]/[6, 3, 1, 8, 5, 2, 4, 7, 0]/[8, 1, 4, 6, 3, 0, 7, 5, 2]/
[0, 6, 3, 7, 2, 4, 8, 1, 5]/[1, 8, 5, 2, 4, 7, 0, 3, 6]/[2, 5, 8, 0, 7, 3, 1, 6, 4]/[3, 7, 0, 4, 6, 1, 5, 2, 8]/[4, 2, 7, 5, 1, 8, 6, 0, 3]/[6, 3, 1, 8, 5, 2, 4, 7, 0]/[8, 1, 4, 6, 3, 0, 7, 5, 2]/
[0, 6, 3, 7, 2, 4, 8, 1, 5]/[2, 5, 8, 1, 4, 6, 3, 0, 7]/[3, 7, 0, 4, 6, 1, 5, 2, 8]/[4, 2, 7, 5, 1, 8, 0, 3, 6]/[5, 8, 2, 0, 7, 3, 1, 6, 4]/[6, 3, 1, 8, 5, 2, 4, 7, 0]/[8, 1, 4, 6, 3, 0, 7, 5, 2]/
[0, 7, 4, 2, 5, 8, 1, 3, 6]/[1, 3, 8, 6, 4, 2, 0, 5, 7]/[2, 5, 7, 0, 3, 6, 4, 1, 8]/[3, 0, 6, 8, 1, 5, 7, 2, 4]/[4, 6, 1, 3, 7, 0, 2, 8, 5]/[6, 2, 5, 7, 0, 3, 8, 4, 1]/[7, 4, 0, 5, 8, 1, 3, 6, 2]/
[0, 7, 4, 2, 5, 8, 1, 3, 6]/[2, 5, 7, 0, 3, 6, 4, 1, 8]/[3, 0, 6, 8, 1, 5, 7, 2, 4]/[4, 6, 1, 3, 7, 0, 8, 5, 2]/[5, 1, 8, 4, 2, 7, 3, 6, 0]/[6, 3, 0, 7, 4, 2, 5, 8, 1]/[8, 2, 5, 1, 6, 4, 0, 7, 3]/
[0, 7, 4, 2, 5, 8, 1, 3, 6]/[2, 5, 7, 0, 3, 6, 4, 1, 8]/[3, 6, 0, 5, 8, 1, 7, 4, 2]/[5, 1, 8, 4, 2, 7, 3, 6, 0]/[6, 0, 3, 7, 4, 2, 8, 5, 1]/[7, 4, 1, 8, 0, 3, 6, 2, 5]/[8, 2, 5, 1, 6, 4, 0, 7, 3]/
[0, 7, 4, 2, 5, 8, 1, 3, 6]/[2, 5, 7, 0, 3, 6, 4, 1, 8]/[3, 6, 2, 5, 8, 0, 7, 4, 1]/[5, 1, 8, 4, 2, 7, 3, 6, 0]/[6, 4, 1, 7, 0, 3, 8, 2, 5]/[7, 3, 0, 6, 4, 1, 5, 8, 2]/[8, 2, 5, 1, 6, 4, 0, 7, 3]/
[0, 7, 4, 2, 5, 8, 1, 3, 6]/[2, 5, 7, 0, 3, 6, 4, 1, 8]/[4, 6, 1, 3, 7, 0, 2, 8, 5]/[5, 1, 8, 4, 2, 7, 3, 6, 0]/[6, 3, 0, 8, 1, 5, 7, 2, 4]/[7, 0, 3, 6, 4, 1, 8, 5, 2]/[8, 2, 5, 1, 6, 4, 0, 7, 3]/
[1, 3, 8, 6, 4, 2, 0, 5, 7]/[2, 5, 7, 1, 3, 8, 6, 4, 0]/[3, 0, 6, 8, 1, 5, 7, 2, 4]/[4, 6, 1, 3, 7, 0, 2, 8, 5]/[5, 7, 0, 4, 8, 1, 3, 6, 2]/[6, 2, 5, 7, 0, 4, 8, 1, 3]/[8, 4, 2, 0, 5, 7, 1, 3, 6]/
[1, 4, 7, 0, 8, 5, 2, 6, 3]/[2, 5, 8, 6, 3, 0, 7, 1, 4]/[3, 6, 2, 7, 1, 4, 8, 5, 0]/[4, 7, 1, 8, 5, 2, 0, 3, 6]/[5, 2, 6, 3, 0, 8, 1, 4, 7]/[6, 0, 5, 1, 4, 7, 3, 8, 2]/[8, 3, 0, 4, 7, 1, 6, 2, 5]/
[1, 4, 8, 3, 0, 7, 5, 2, 6]/[2, 6, 3, 1, 8, 5, 0, 4, 7]/[4, 2, 7, 5, 1, 8, 6, 0, 3]/[5, 8, 2, 0, 7, 3, 1, 6, 4]/[6, 3, 1, 8, 5, 2, 4, 7, 0]/[7, 5, 0, 2, 4, 6, 8, 3, 1]/[8, 1, 4, 6, 3, 0, 7, 5, 2]/
[1, 5, 8, 2, 4, 7, 3, 0, 6]/[2, 7, 5, 3, 8, 0, 4, 6, 1]/[3, 6, 2, 7, 1, 4, 8, 5, 0]/[4, 0, 7, 5, 2, 6, 1, 3, 8]/[5, 2, 6, 1, 3, 8, 0, 7, 4]/[7, 1, 4, 6, 0, 3, 5, 8, 2]/[8, 3, 0, 4, 7, 1, 6, 2, 5]/
[1, 6, 4, 7, 0, 3, 5, 2, 8]/[2, 5, 7, 1, 3, 8, 6, 4, 0]/[4, 1, 8, 5, 2, 6, 3, 0, 7]/[5, 8, 0, 3, 6, 2, 7, 1, 4]/[6, 3, 1, 4, 8, 0, 2, 7, 5]/[7, 0, 3, 6, 4, 1, 8, 5, 2]/[8, 4, 2, 0, 5, 7, 1, 3, 6]/
[2, 8, 3, 7, 4, 1, 5, 0, 6]/[3, 6, 2, 5, 8, 0, 7, 4, 1]/[4, 0, 7, 3, 1, 6, 8, 5, 2]/[5, 1, 8, 4, 2, 7, 3, 6, 0]/[6, 3, 0, 2, 7, 5, 1, 8, 4]/[7, 4, 1, 8, 0, 3, 6, 2, 5]/[8, 2, 5, 1, 6, 4, 0, 7, 3]/
Alle Angaben ohne Gewähr.
Es gibt 352 Möglichkeiten, 9 Damen auf einem 9x9-Brett aufzustellen, so dass sie einander nicht bedrohen.
Es gibt 1552 Möglichkeiten, sieben disjunkte Lösungen auszuwählen. Es ist nicht möglich, acht oder neun disjunkte Lösungen auszuwählen.
Mit der zusätzlichen Sudoku-Bedingung (in jedem 3x3-Block steht genau eine Dame) verbleiben noch 144 von 352 Lösungen, und es gibt nur noch 24 Möglichkeiten, sieben disjunkte Lösungen auszuwählen:
[0, 4, 6, 8, 3, 1, 7, 5, 2]/[1, 8, 5, 2, 4, 7, 0, 3, 6]/[2, 5, 7, 4, 0, 8, 6, 1, 3]/[3, 0, 8, 5, 2, 6, 1, 7, 4]/[4, 7, 0, 3, 6, 2, 5, 8, 1]/[6, 3, 1, 7, 5, 0, 2, 4, 8]/[7, 2, 4, 1, 8, 5, 3, 6, 0]/
[0, 4, 6, 8, 3, 1, 7, 5, 2]/[2, 5, 8, 1, 4, 6, 3, 0, 7]/[4, 1, 7, 2, 6, 3, 0, 8, 5]/[5, 7, 2, 0, 8, 4, 1, 3, 6]/[6, 3, 1, 7, 5, 0, 2, 4, 8]/[7, 0, 3, 6, 2, 5, 8, 1, 4]/[8, 2, 5, 3, 0, 7, 4, 6, 1]/
[0, 4, 6, 8, 3, 1, 7, 5, 2]/[2, 6, 3, 1, 8, 4, 0, 7, 5]/[3, 1, 8, 4, 0, 7, 5, 2, 6]/[4, 2, 7, 5, 1, 8, 6, 0, 3]/[5, 8, 2, 0, 7, 3, 1, 6, 4]/[6, 3, 1, 7, 5, 0, 2, 4, 8]/[7, 5, 0, 2, 4, 6, 8, 3, 1]/
[0, 5, 7, 2, 6, 3, 1, 8, 4]/[2, 8, 5, 1, 4, 6, 0, 3, 7]/[3, 6, 2, 7, 1, 4, 8, 5, 0]/[4, 1, 8, 0, 5, 7, 2, 6, 3]/[6, 0, 3, 5, 8, 2, 4, 7, 1]/[7, 2, 4, 8, 0, 5, 3, 1, 6]/[8, 3, 0, 4, 7, 1, 6, 2, 5]/
[0, 5, 8, 4, 1, 7, 2, 6, 3]/[1, 6, 4, 0, 8, 3, 5, 7, 2]/[2, 8, 5, 3, 0, 6, 4, 1, 7]/[4, 7, 0, 8, 3, 1, 6, 2, 5]/[5, 2, 6, 1, 7, 4, 0, 3, 8]/[6, 0, 3, 7, 4, 2, 8, 5, 1]/[8, 3, 1, 6, 2, 5, 7, 0, 4]/
[0, 5, 8, 4, 1, 7, 2, 6, 3]/[1, 7, 4, 2, 8, 5, 3, 0, 6]/[3, 6, 2, 7, 5, 0, 8, 1, 4]/[4, 8, 1, 3, 6, 2, 7, 5, 0]/[5, 2, 6, 1, 7, 4, 0, 3, 8]/[6, 1, 3, 5, 0, 8, 4, 2, 7]/[7, 3, 0, 6, 4, 1, 5, 8, 2]/
[0, 5, 8, 4, 1, 7, 2, 6, 3]/[2, 8, 3, 7, 4, 1, 5, 0, 6]/[3, 6, 2, 5, 8, 0, 7, 4, 1]/[4, 1, 7, 0, 3, 6, 8, 5, 2]/[5, 2, 6, 1, 7, 4, 0, 3, 8]/[6, 3, 0, 2, 5, 8, 1, 7, 4]/[7, 4, 1, 8, 0, 3, 6, 2, 5]/
[0, 6, 3, 5, 8, 1, 4, 2, 7]/[1, 8, 5, 2, 6, 3, 0, 7, 4]/[2, 5, 7, 1, 3, 8, 6, 4, 0]/[3, 1, 6, 8, 0, 4, 7, 5, 2]/[4, 7, 1, 6, 2, 5, 8, 0, 3]/[6, 3, 0, 7, 4, 2, 5, 8, 1]/[8, 4, 2, 0, 5, 7, 1, 3, 6]/
[0, 6, 3, 7, 2, 4, 8, 1, 5]/[1, 4, 7, 0, 8, 5, 2, 6, 3]/[2, 5, 8, 6, 1, 3, 7, 0, 4]/[3, 7, 0, 4, 6, 1, 5, 2, 8]/[4, 8, 1, 5, 7, 2, 0, 3, 6]/[5, 2, 6, 3, 0, 8, 1, 4, 7]/[6, 0, 5, 1, 4, 7, 3, 8, 2]/
[0, 6, 3, 7, 2, 4, 8, 1, 5]/[1, 4, 7, 0, 8, 5, 2, 6, 3]/[2, 8, 5, 1, 4, 6, 0, 3, 7]/[3, 7, 0, 4, 6, 1, 5, 2, 8]/[5, 2, 8, 3, 0, 7, 1, 4, 6]/[6, 3, 1, 8, 5, 2, 4, 7, 0]/[8, 1, 4, 6, 3, 0, 7, 5, 2]/
[0, 6, 3, 7, 2, 4, 8, 1, 5]/[1, 5, 8, 2, 4, 7, 3, 0, 6]/[2, 4, 7, 1, 8, 5, 0, 6, 3]/[3, 7, 0, 4, 6, 1, 5, 2, 8]/[5, 2, 6, 3, 0, 8, 1, 4, 7]/[6, 3, 1, 8, 5, 2, 4, 7, 0]/[8, 1, 4, 6, 3, 0, 7, 5, 2]/
[0, 6, 3, 7, 2, 4, 8, 1, 5]/[1, 8, 5, 2, 4, 7, 0, 3, 6]/[2, 5, 8, 0, 7, 3, 1, 6, 4]/[3, 7, 0, 4, 6, 1, 5, 2, 8]/[4, 2, 7, 5, 1, 8, 6, 0, 3]/[6, 3, 1, 8, 5, 2, 4, 7, 0]/[8, 1, 4, 6, 3, 0, 7, 5, 2]/
[0, 6, 3, 7, 2, 4, 8, 1, 5]/[2, 5, 8, 1, 4, 6, 3, 0, 7]/[3, 7, 0, 4, 6, 1, 5, 2, 8]/[4, 2, 7, 5, 1, 8, 0, 3, 6]/[5, 8, 2, 0, 7, 3, 1, 6, 4]/[6, 3, 1, 8, 5, 2, 4, 7, 0]/[8, 1, 4, 6, 3, 0, 7, 5, 2]/
[0, 7, 4, 2, 5, 8, 1, 3, 6]/[1, 3, 8, 6, 4, 2, 0, 5, 7]/[2, 5, 7, 0, 3, 6, 4, 1, 8]/[3, 0, 6, 8, 1, 5, 7, 2, 4]/[4, 6, 1, 3, 7, 0, 2, 8, 5]/[6, 2, 5, 7, 0, 3, 8, 4, 1]/[7, 4, 0, 5, 8, 1, 3, 6, 2]/
[0, 7, 4, 2, 5, 8, 1, 3, 6]/[2, 5, 7, 0, 3, 6, 4, 1, 8]/[3, 0, 6, 8, 1, 5, 7, 2, 4]/[4, 6, 1, 3, 7, 0, 8, 5, 2]/[5, 1, 8, 4, 2, 7, 3, 6, 0]/[6, 3, 0, 7, 4, 2, 5, 8, 1]/[8, 2, 5, 1, 6, 4, 0, 7, 3]/
[0, 7, 4, 2, 5, 8, 1, 3, 6]/[2, 5, 7, 0, 3, 6, 4, 1, 8]/[3, 6, 0, 5, 8, 1, 7, 4, 2]/[5, 1, 8, 4, 2, 7, 3, 6, 0]/[6, 0, 3, 7, 4, 2, 8, 5, 1]/[7, 4, 1, 8, 0, 3, 6, 2, 5]/[8, 2, 5, 1, 6, 4, 0, 7, 3]/
[0, 7, 4, 2, 5, 8, 1, 3, 6]/[2, 5, 7, 0, 3, 6, 4, 1, 8]/[3, 6, 2, 5, 8, 0, 7, 4, 1]/[5, 1, 8, 4, 2, 7, 3, 6, 0]/[6, 4, 1, 7, 0, 3, 8, 2, 5]/[7, 3, 0, 6, 4, 1, 5, 8, 2]/[8, 2, 5, 1, 6, 4, 0, 7, 3]/
[0, 7, 4, 2, 5, 8, 1, 3, 6]/[2, 5, 7, 0, 3, 6, 4, 1, 8]/[4, 6, 1, 3, 7, 0, 2, 8, 5]/[5, 1, 8, 4, 2, 7, 3, 6, 0]/[6, 3, 0, 8, 1, 5, 7, 2, 4]/[7, 0, 3, 6, 4, 1, 8, 5, 2]/[8, 2, 5, 1, 6, 4, 0, 7, 3]/
[1, 3, 8, 6, 4, 2, 0, 5, 7]/[2, 5, 7, 1, 3, 8, 6, 4, 0]/[3, 0, 6, 8, 1, 5, 7, 2, 4]/[4, 6, 1, 3, 7, 0, 2, 8, 5]/[5, 7, 0, 4, 8, 1, 3, 6, 2]/[6, 2, 5, 7, 0, 4, 8, 1, 3]/[8, 4, 2, 0, 5, 7, 1, 3, 6]/
[1, 4, 7, 0, 8, 5, 2, 6, 3]/[2, 5, 8, 6, 3, 0, 7, 1, 4]/[3, 6, 2, 7, 1, 4, 8, 5, 0]/[4, 7, 1, 8, 5, 2, 0, 3, 6]/[5, 2, 6, 3, 0, 8, 1, 4, 7]/[6, 0, 5, 1, 4, 7, 3, 8, 2]/[8, 3, 0, 4, 7, 1, 6, 2, 5]/
[1, 4, 8, 3, 0, 7, 5, 2, 6]/[2, 6, 3, 1, 8, 5, 0, 4, 7]/[4, 2, 7, 5, 1, 8, 6, 0, 3]/[5, 8, 2, 0, 7, 3, 1, 6, 4]/[6, 3, 1, 8, 5, 2, 4, 7, 0]/[7, 5, 0, 2, 4, 6, 8, 3, 1]/[8, 1, 4, 6, 3, 0, 7, 5, 2]/
[1, 5, 8, 2, 4, 7, 3, 0, 6]/[2, 7, 5, 3, 8, 0, 4, 6, 1]/[3, 6, 2, 7, 1, 4, 8, 5, 0]/[4, 0, 7, 5, 2, 6, 1, 3, 8]/[5, 2, 6, 1, 3, 8, 0, 7, 4]/[7, 1, 4, 6, 0, 3, 5, 8, 2]/[8, 3, 0, 4, 7, 1, 6, 2, 5]/
[1, 6, 4, 7, 0, 3, 5, 2, 8]/[2, 5, 7, 1, 3, 8, 6, 4, 0]/[4, 1, 8, 5, 2, 6, 3, 0, 7]/[5, 8, 0, 3, 6, 2, 7, 1, 4]/[6, 3, 1, 4, 8, 0, 2, 7, 5]/[7, 0, 3, 6, 4, 1, 8, 5, 2]/[8, 4, 2, 0, 5, 7, 1, 3, 6]/
[2, 8, 3, 7, 4, 1, 5, 0, 6]/[3, 6, 2, 5, 8, 0, 7, 4, 1]/[4, 0, 7, 3, 1, 6, 8, 5, 2]/[5, 1, 8, 4, 2, 7, 3, 6, 0]/[6, 3, 0, 2, 7, 5, 1, 8, 4]/[7, 4, 1, 8, 0, 3, 6, 2, 5]/[8, 2, 5, 1, 6, 4, 0, 7, 3]/
Alle Angaben ohne Gewähr.