since a puzzle can be represented as a graph whose vertices are the clues and whose edges are pairs of clues that share a unit, i was wondering how many components a puzzle with a unique solution can have? and also what can be the maximum size of the components.
here is a puzzle with 4 components, 3 of size 1 and 1 of size 20:
- Code: Select all
1 . . . . . . . .
. . . . 3 5 2 1 .
. . . . 8 2 7 . .
. . 7 . 4 . 1 3 .
. . 6 . . . 9 5 .
. . 8 . 5 3 . . .
. . . 6 1 4 . . .
. 3 . . . . . . .
. . . . . . . . 2
1............3521.....827....7.4.13...6...95...8.53......614....3...............2