BUG-Lite and RodHagglund's Guardians
Consider the following BUG-Lite grid (
an RW example)
000070500000001060040560310012000600000000103009000420081040730050700000006038000
- Code: Select all
1 6 38 |#3489 7 #349 | 5 489 2
35 *29 357 | 34 *29+8 1 |#89 6 47
*29 4 78 | 5 6 *29 | 3 1 78
--------------+--------------------+--------------
458 1 2 | 348 58 34 | 6 7 9
4568 7 45 |*29+468 #2589 *29+4 | 1 58 3
568 3 9 | 68 1 7 | 4 2 58
--------------+--------------------+--------------
*29 8 1 |*29 4 5 | 7 3 6
34 5 34 | 7 *29 6 |*29+8 89 1
7 *29 6 | 1 3 8 |*29 45 45
According to the BUG-Lite+N principle, we know at least one of the extra candidates in r2c5, r5c4, r5c6, and r8c7 must be true. But finding a common exclusion for six extra candidates is not an easy task.
However, as a corollary to the BUG-Lite+N principle, we also know at least one of the BUG candidates must be excludible from the cells with extra candidates. We get no help from the 2s, because every row, column, and box contains either 0 or 2 candidates. But with a placement of digit 9 in either r1c4, r1c6, r2c7, or r5c3, the deadly pattern is avoided ... and r2c5 "sees" all four of those cells. Therefore, r2c5<>9 is a valid exclusion.
Those familiar with RodHagglund's
Broken Wing may see the four cells (marked with '#') as "guardians", any one of which being true prevents the deadly BUG-Lite pattern.
[edit: While I'm sure the theory is sound, the example stinks ... because I missed the 9 in r8c8.
]
P.S. Why the heck aren't we getting line-wrap on this page?