One thing possibly worth noticing about the above puzzle with a very large number of expansion steps within T&E(3) is, if you consider both the original puzzle (or its BRT-expand) and the max-expanded one (1st line), they have the same resolution state after Singles, whips[1] and Pairs - and the same tridagon (with the same unique guardian).
- Code: Select all
+----------------------+----------------------+----------------------+
! 1 248# 3 ! 45 2458 6 ! 7 248# 9 !
! 248# 5 7 ! 19 248 19 ! 248# 36 36 !
! 9 6 248# ! 3 248 7 ! 5 1 248# !
+----------------------+----------------------+----------------------+
! 248 248 248 ! 56 9 3 ! 1 56 7 !
! 5 39 6 ! 7 1 2 ! 489 348 348 !
! 7 39 1 ! 456 45 8 ! 29 2356 2356 !
+----------------------+----------------------+----------------------+
! 3 248# 9 ! 128 7 145 ! 6 2458#@ 12458 !
! 6 7 248# ! 128 3 145 ! 248# 9 12458 !
! 248# 1 5 ! 289 6 49 ! 3 7 248# !
+----------------------+----------------------+----------------------+
tridagon for digits 2, 4 and 8 in blocks:
b9, with cells (marked #): r7c8 (target cell, marked @), r9c9, r8c7
b7, with cells (marked #): r7c2, r9c1, r8c3
b3, with cells (marked #): r1c8, r3c9, r2c7
b1, with cells (marked #): r1c2, r3c3, r2c1
==> r7c8≠2,4,8
naked-single ==> r7c8=5
It means we've been able to add 10 independent clues with the following BRT-expansions, for a total of 14 clues added, without essentially changing the puzzle.
From:
- Code: Select all
+-------+-------+-------+
! 1 . . ! . . . ! 7 . 9 !
! . 5 . ! . . . ! . . . !
! 9 . . ! 3 . . ! 5 1 . !
+-------+-------+-------+
! . . . ! . 9 . ! . . 7 !
! 5 . 6 ! . . 2 ! . . . !
! . . 1 ! . . 8 ! . . . !
+-------+-------+-------+
! 3 . . ! . 7 . ! 6 . . !
! . . . ! . 3 . ! . 9 . !
! . 1 5 ! . 6 . ! 3 . . !
+-------+-------+-------+
to:
- Code: Select all
+-------+-------+-------+
! 1 . 3 ! . . 6 ! 7 . 9 !
! . 5 7 ! . . . ! . . . !
! 9 6 . ! 3 . 7 ! 5 1 . !
+-------+-------+-------+
! . . . ! . 9 3 ! 1 . 7 !
! 5 . 6 ! 7 1 2 ! . . . !
! 7 . 1 ! . . 8 ! . . . !
+-------+-------+-------+
! 3 . 9 ! . 7 . ! 6 . . !
! 6 7 . ! . 3 . ! . 9 . !
! . 1 5 ! . 6 . ! 3 7 . !
+-------+-------+-------+
.