Where are the BUGs?

[David Bryant]

I've been having some trouble finding the "BUG" patterns in this week's special collection. I did find a BUG+1 pattern in the puzzle for July 9th, but I solved it three different ways before I figured out how to see a BUG.

Today's puzzle is a case in point. After doing the usual stuff I arrived here.

Code: Select all

 456   259    3     1   2469   247   479   249    8
  1    289    24   278  24679   3     5    249  4679
  46   289    7     28  2469    5     1     3    469
  89    3     6     27   247  2489    49    1     5
  89    4     5     6     1     89    3     7     2
  2     7     1     3     5     49    6     8     49
  7     6     9     4     8     1     2     5     3
  45    25    8     9     3     27    47    6     1
  3     1     24    5     27    6     8     49   479

At this point I spotted a very nice DIC proceeding from r8c2.

A. r8c2 = 5 ==> r1c1 = 5 ==> r3c1 = 6
B. r8c2 = 5 ==> r9c3 = 2 ==> r9c5 = 7 ==> r2c9 = 7 ==> r3c9 = 6

With r8c2 = 2 the rest is singles all the way.

Can somebody point out the "BUG" in this puzzle? dcb

PS Proceeding from the same point I also tried setting r5c6 = 8, based on the "UR" in r45c16 ... this led me through another "UR" (r23c24) pattern that got to the solution, but I still didn't find a "BUG".

[Ruud]

Hi David,

The trouble with BUG is that it is usually the last step before the final cascade of singles. Sudokus as complex as the Daily Nightmares can be solved in many ways, and I can only hope that the solving path you choose leads to to the BUG. Since DIC's are not on my list, using them will lead you away from the BUG.

About todays Nightmare:

Singles and intersections bring you here:

Code: Select all

.------------------.------------------.------------------.
| 456   259   3    | 1     24679 2479 | 479   249   8    |
| 1     289   24   | 278   24679 3    | 5     249   4679 |
| 46    289   7    | 28    2469  5    | 1     3     469  |
:------------------+------------------+------------------:
| 89    3     6    | 27    2479  24789| 49    1     5    |
| 89    4     5    | 6     1     89   | 3     7     2    |
| 2     7     1    | 3     5     49   | 6     8     49   |
:------------------+------------------+------------------:
| 7     6     9    | 4     8     1    | 2     5     3    |
| 45    25    8    | 9     3     27   | 47    6     1    |
| 3     1     24   | 5     27    6    | 8     49    479  |
'------------------'------------------'------------------'

My solver now continues:
finned X-Wing removes 2 from R1C6
finned X-Wing removes 4 from R2C9
finned X-Wing removes 7 from R1C5
X-Wing removes 7 from R4C6
finned X-Wing removes 9 from R1C6
intersection removes 9 from R4C5
uniqueness 1 removes 89 from R4C6
a few singles
naked pair 47 in row 1
X-Wing removes 4 from R2C5
XY-Wing removes 7 from R2C4
single and intersection
hidden pair 67 in row 2
hidden pair 28 in row 3
uniqueness 1 removes 28 from R2C2 (leaves single 9)
a few singles

brings us to da BUG:

Code: Select all

.------------.------------.------------.
| 56  25  3  | 1   69  47 | 47  29  8  |
| 1   9   24 | 8   67  3  | 5   24  67 |
| 46  8   7  | 2   469 5  | 1   3   69 |
:------------+------------+------------:
| 8   3   6  | 7   24  24 | 9   1   5  |
| 9   4   5  | 6   1   8  | 3   7   2  |
| 2   7   1  | 3   5   9  | 6   8   4  |
:------------+------------+------------:
| 7   6   9  | 4   8   1  | 2   5   3  |
| 45  25  8  | 9   3   27 | 47  6   1  |
| 3   1   24 | 5   27  6  | 8   49  79 |
'------------'------------'------------'

You see how many things you could have missed or done differently?

cheers,
Ruud

[David Bryant]

Thanks for the explanation, Ruud.

I went back through some of the earlier puzzles and managed to work a couple of those down to a BUG + 1 pattern by relying heavily on the "uniqueness" of each solution. That probably explains my problem -- like Chuck B, I usually try to avoid making that assumption unless I'm completely stymied otherwise.

It makes sense that if the final blow (BUG + 1) depends on uniquity, one must also use that tool all along the way. dcb

[dejsmith]

Thank goodness it was not just me! I could not find any bugs all week (I am two days behind, though) & got very frustrated having to rely on forcing chains, which really do not improve my solving skills at all. I personally love uniquity & consider it a valid, logical technique; so I'll recheck one or two to see if I missed some. Thanks Rudd & David for your explanations. I look forward to our fishing expedition next week; but am quite concerned that I will meet up with some big sharks that will refuse to be caught & may catch me!

Dave