The New Sudoku Players' Forum

[scrose]

This puzzle came from a page-a-day calendar. Unfortunately, I have already discarded the packaging and all the non-puzzle pages, so I can no longer remember the specific name of this calendar. I assume it is related to the Daily Telegraph because each page is footnoted with their address. In any case, this particular puzzle is from the January 6/7 page.

Original:

Code: Select all

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

Where I'm stuck:

Code: Select all

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

At this point I had to start using pencilmarks. After staring at them for a while, I found an x-wing, which didn't appear to move the puzzle any further. So I threw in the towel and dumped the whole thing into Angus's program. It confirmed there is only one solution, but could only boil the pencilmarks down to the following.

Code: Select all

 16  3   5    | 2  8 7  | 146 69   149
 18  2   9    | 4  3 6  | 157 78   158
 7   4   68   | 1  9 5  | 68  3    2
--------------+---------+--------------
 249 1   247  | 5  6 48 | 27  789  3
 49  678 347  | 39 2 48 | 15  6789 15
 5   68  236  | 39 7 1  | 26  4    89
--------------+---------+--------------
 3   9   48   | 6  1 2  | 48  5    7
 24  67  2467 | 8  5 3  | 9   1    46
 68  5   1    | 7  4 9  | 3   2    68

Could someone please explain (preferably, in detail) what the next step(s) should be? My apologies if this particular puzzle has been discussed earlier; please direct me to the appropriate thread (which I was unable to find via searching.) Thanks in advance.

[daj95376]

There is an XYZ-Wing for [r4c8] that causes [r5c8]<>8 ... but isn't of any real help.

At this point, a Unique Rectangle Type ??? is possible. You have the <15> pair in [r5c79]. If you look at [r2], you'll see [r2c7]=<157> and [r2c9]=<158>. Also, the only place in [r2] that contains <5> is [r2c79]. This means that the value <1> can be eliminated from [r2c79]. The puzzle then solves with a cascade of singles.

Code: Select all

 *-----------------------------------------------------------*
 | 16    3     5     | 2     8     7     | 146   69    149   |
 | 18    2     9     | 4     3     6     | 57-1  78    58-1  |
 | 7     4     68    | 1     9     5     | 68    3     2     |
 |-------------------+-------------------+-------------------|
 | 249   1     247   | 5     6     48    | 27    789   3     |
 | 49    678   347   | 39    2     48    |*15    6789 *15    |
 | 5     68    236   | 39    7     1     | 26    4     89    |
 |-------------------+-------------------+-------------------|
 | 3     9     48    | 6     1     2     | 48    5     7     |
 | 24    67    2467  | 8     5     3     | 9     1     46    |
 | 68    5     1     | 7     4     9     | 3     2     68    |
 *-----------------------------------------------------------*


[scrose]

Thanks very much for your help. I just finished reading keith's explanation of unique rectangles. I kind-of sort-of understand. Hopefully I'll be able to recognize this pattern if I see it again.

[re'born]

An alternative solution is an xy-chain:
[r1c9]-9-[r1c8]-6-[r1c1]-1-[r2c1]-8-[r9c1]-6-[r9c9]-8-[r6c9]-9-[r1c9]

This implies that r1c9 <> 9 and the puzzle then solves with singles.

P.S. I prefer the UR solution (which, incidentally, works without using the XYZ-wing first), but some don't accepts those type of solutions.

[Edit: A shorter xy-chain is:

[r2c7]-7-[r2c8]-8-[r3c7]-6-[r6c7]-2-[r4c7]-7-[r2c7]

This implies that r2c7 <> 7 and this solves the puzzle.]

[daj95376]

rep'nA, Interesting how you chose to represent the first XY-Chain. My solver found essentially the same chain, but found two eliminations because the chain is traced differently. Simply different starting points.

9-[r1c8]-6-[r1c1]-1-[r2c1]-8-[r9c1]-6-[r9c9]-8-[r6c9]-9-( [r1c9] & [r4c8] )

[re'born]

rep'nA, Interesting how you chose to represent the first XY-Chain. My solver found essentially the same chain, but found two eliminations because the chain is traced differently. Simply different starting points.

9-[r1c8]-6-[r1c1]-1-[r2c1]-8-[r9c1]-6-[r9c9]-8-[r6c9]-9-( [r1c9] & [r4c8] )

My 'choice' of how to represent the chain is mostly based on ignorance. I've never felt comfortable with converting the chains I find into nice loop notation. In this case, I went to Jeff's xy-chain post and copied one of the examples. It bothered me that I could only show 1 elimination with the chain, but then felt relieved once I saw that I only needed 1 to solve the puzzle. The same thing happened in my second chain which should make 3 eliminations, of which only 1 is needed.

[daj95376]

My 'choice' of how to represent the chain is mostly based on ignorance. I've never felt comfortable with converting the chains I find into nice loop notation. In this case, I went to Jeff's xy-chain post and copied one of the examples. It bothered me that I could only show 1 elimination with the chain, but then felt relieved once I saw that I only needed 1 to solve the puzzle. The same thing happened in my second chain which should make 3 eliminations, of which only 1 is needed.

rep'nA.

I learned about XY-Chains from the Sadman website. He has a simple explanation and an example that was easy to visualize. So, that's how I wrote my solver. It wasn't until I saw your chain and went to Jeff's thread that I realized there was a different approach. That's why I commented. I was wondering if I was doing it wrong. Thanks for sharing your views.

PS: MY chain notation is 'home grown'. I take what makes sense from the 'official' threads, and I try to come as close as possible to matching it. Maybe it's time that someone started the Ultimate Chain Notation Guide. If done right, maybe a nice summary could be presented about each chain and its notation.