Extra Hard Daily Sudoku for Feb 5 from BrainBusters

[lac]

This is Extra Hard Daily Sudoku for Feb 5 from

http://www.brainbashers.com/sudoku.asp


It's not nightmare standard, but it is hard.

Code: Select all

.-----------------------.-----------------------.-----------------------.
|.      .       3       |7      .       1       |8      .       .       |
|.      .       .       |9      5       2       |.      .       .       |
|1      .       .       |.      3       .       |.      .       7       |
:-----------------------+-----------------------+-----------------------:
|6      8       .       |.      .       .       |.      9       5       |
|.      7       2       |.      .       .       |1      8       .       |
|4      3       .       |.      .       .       |.      6       2       |
:-----------------------+-----------------------+-----------------------:
|2      .       .       |.      8       .       |.      .       9       |
|.      .       .       |5      7       6       |.      .       .       |
|.      .       7       |2      .       4       |5      .       .       |
'-----------------------'-----------------------'-----------------------'

I solved it after finding one forcing chain, from c7r4 to c7r7

But what puzzles me is that the brainbusters site lists which techniques
it thinks you need to use to solve the puzzle. Forcing chains is not on
its list.

Here is its list:

Techniques Required:
Forced Moves
Pinned Squares
Locked Sets (x3)
Intersection Removal (x1)
Unique Rectangles (x2)
XY-Wing (x2)

But I cannot see this. I don't see any unique rectangles at all, and
if, as I suspect, it is considering c5r1, c9r1, c5r5, c9r5 a unique
rectangle, then it ought not to. The correct number just happens to
be the one that was filled in, but these values lie in 4 houses, not 2,
and so you cannot use uniqueness in this case.

Am I just missing something?

Laura

[Ruud]

Hi Laura,

This puzzle can be solved with singles, naked & hidden pairs, and a single multi-coloring stap.

There is a moment where you can see a uniqueness rectangle type 4 in the lower corner, for digits{3,8}. The 3's can be eliminated, but you do not NEED it to solve the puzzle.

In many cases, my Nightmares also show uniqueness rectangles as a "promising" way out. You will, most of the time, be able to solve the Nightmare without it, but they're there if you want to use them...

Ruud.

[David Bryant]

I don't see any unique rectangles at all ...

Hi, Laura!

I did manage to find a "unique rectangle", and I could even use it to solve the rest of the puzzle. But
I didn't spot any XY-Wings, and I'm not even sure what an "Intersection Removal" is.

Anyway, after making a bunch of moves (mostly sole candidates, and unique positions) I arrived
at this spot.

Code: Select all

*------------------------------------------*
| 59  259  3  |  7  46   1  |  8  25   46  |
|  7  46   8  |  9   5   2  | 346 134 1346 |
|  1 2456 456 | 46   3   8  |  9  25    7  |
|-------------+-------------+--------------|
|  6   8   1  | 34   2   7  | 34   9    5  |
| 59   7   2  | 346 46  59  |  1   8   34  |
|  4   3  59  |  8   1  59  |  7   6    2  |
|-------------+-------------+--------------|
|  2  456 456 |  1   8   3  | 46   7    9  |
| 38  149 49  |  5   7   6  |  2  134 1348 |
| 38  16   7  |  2   9   4  |  5  13  1368 |
*------------------------------------------*

There's a binary chain in the "6"s, leading from r2c7 - r7c7 - r9c9 - r9c2. So we can use a simple
parity argument to eliminate the possible "6" at r2c2. Now it looks like this.

Code: Select all

*------------------------------------------*
| 59  259  3  |  7  46   1  |  8  25   46  |
|  7   4   8  |  9   5   2  | 36  13   136 |
|  1  256 56  | 46   3   8  |  9  25    7  |
|-------------+-------------+--------------|
|  6   8   1  | 34   2   7  | 34   9    5  |
| 59   7   2  | 346 46  59  |  1   8   34  |
|  4   3  59  |  8   1  59  |  7   6    2  |
|-------------+-------------+--------------|
|  2  56  456 |  1   8   3  | 46   7    9  |
| 38  19  49  |  5   7   6  |  2  134 1348 |
| 38  16   7  |  2   9   4  |  5  13  1368 |
*------------------------------------------*

The "non-unique rectangle" is on the digits "2" and "5", at r1c2, r3c2, r1c8, and r3c8. We can
use it to solve the puzzle as follows.

-- Either "9" appears at r1c2, or "6" appears at r3c2; otherwise the solution would not be unique.

-- Therefore there's either a "5" at r1c1 or r3c3, and there cannot be a "5" at r1c2 or r3c2.

-- We conclude that r7c2 = 5, and the rest of the puzzle falls apart. (It would fall apart anyway, just
because of the "4" at r2c2. But the "5" doesn't hurt anything ...)

I'm not familiar with "brainbashers" and the terminology they use. I'll have to take a peek at their
site some time -- thanks for the tip. dcb