## Very Hard - from Times Website

All about puzzles in newspapers, magazines, and books
I think that all of the regular contributors to this thread would welcome Wayne's explanation of how the original puzzle could be solved logically.

The Nishio appears to be another, infrequently used and never used in The Times puzzles, technique to solve Sudokus.

I believe that the logical explanation to solve this puzzle is one of several techniques that exist, but are still relatively private knowledge (q.v. the number of Internet sites describing how to solve the puzzles).

I have a sneaking suspicion that Wayne will not be sharing the technique with us, although I would dearly love to be proved wrong!, and we will have to find it for ourselves...
shakers

Posts: 93
Joined: 10 March 2005

For my pennysworth, I would not like a direct explanation. I understand Wayne's reluctance to give away the secret, and think we would all find it more satisfying if we worked it out amongst ourselves. Perhaps Wayne could nudge us along by narrowing the area of the puzzle we should be looking at - or even telling us which cell is the next one that can be solved. That way we may still find this magical method by collaboration.

I see finding this method as just another level of solving the puzzle - there is a secret and I'd like to work it out, even if I do need a push in the right direction.
Guest

I finally finished this puzzle last night (cannot say solved) by making what I thought was an intuitive leap from the (to me) undecipherable clues. In fact, as I still cannot see any sign of an X Wing fighter now it is complete, I have to believe I just made a lucky guess at a square to guess at, (r3c4 I chose 7) and all flowed from there. I made one mistake, choosing 1 to put into r4c5 because of the talk of 1's and 7's, which had to be swapped with the 5 I had put into the square below it.

I would really like to know what the logic is to solve this one, or at least, as someone else has said, a small section of the puzzle to be directed to to look for a logical next step from the initial sticking point for many of us.
Guest

Ok solved it logically - the "X-Wings" that Wayne refers to are:

look carefully at r1c6, r1c9, r9c6 and r9c9 (forming an X) and then the key is the number 6.

I dont want to say more at this stage in order not to spoil your fun!
su_doku

Posts: 30
Joined: 19 March 2005

su_doku wrote:Ok solved it logically - the "X-Wings" that Wayne refers to are:

look carefully at r1c6, r1c9, r9c6 and r9c9 (forming an X) and then the key is the number 6.

I still haven't quite got it but from your tip all i can conclude is that if a 6 goes in r7c6 then a 6 has to go in r9c9. But then there is no places left for a 6 in row 1. So a 6 cannot go in r7c6. But thats all I got!!
Tim

Posts: 18
Joined: 12 March 2005

I've now just found something else!!

6 cannot go in r7c9, because if it does then a 6 has to go in r9c6 and therefore again there are no places left for a 6 in row 1.

Therefore you can eliminate 6 from r7c9 and therefore the only number that can go in r7c9 is a 9!!
Tim

Posts: 18
Joined: 12 March 2005

Tim, I like it. I think that may be it.

I have no idea what su_doku is talking about. I certainly can't get an answer without trying values first... Perhaps a little more info?
Guest

Though is this deduction possible without T & E?!?
Guest

That is the question!!! I don't know
Tim

Posts: 18
Joined: 12 March 2005

Tim you are on the right track and you've got it but you are unsure of whether its logical.

there is a logical reasoning enabling you to be able to say for sure that 9 and only 9 can go in r7c9. That's where the X-Wings plays a role. Once you convince yourself that with 100% certainty r7c9 = 9 the puzzle opens itself up elegantly.

This is definitely not T&E and hopefully Wayne can confirm.
su_doku

Posts: 30
Joined: 19 March 2005

Hi su_doku, I think I am now with you. If you consider the possible placings of a '6' in the squares you quote at the extremes of th 'X', then it is not possible for r7c9 to be a '6' and thus it must as you say be a 9.

As this does not require assuming that a particular value goes in any square at the extremes of the 'X' then I agree with you that it is not T&E.
SteveF

Posts: 86
Joined: 26 March 2005

### X-Wings v Nishio

I don't see the difference between between the previously-described Nishio technique (deemed beyond the pale by Wayne) and the proposed X-Wings technique. In line with the Nishio technique, I searched the grid for any moves that would make it impossible to place the remaining instances of the value just placed. I found that the following moves could be eliminated:

6 in r4c9, r7c6, r7c9 & r8c6
7 in r1c6, r3c2, r3c3 & r8c4
8 in r2c3

It seems to me that the (perfectly correct) reasoning used by Tim to justify the rejection of a 6 in r7c9 is precisely that used by the Nishio technique. When does a Nishio become an X-Wings and therefore valid? When the cells in question form the vertices of a rectangle?
Sue De Coq

Posts: 93
Joined: 01 April 2005

Su_doku - did you mean r1c7 & r9c7? You wrote c6.
Guest

Yes, I came to the conclusion that Tim was using Nishio too...
Guest

IJ wrote:Su_doku - did you mean r1c7 & r9c7? You wrote c6.

no I meant r1c6 and r9c6 - r1c7 and r9c7 had clues already.

SteveF - you've got it Bingo! Given the possibility of the 6's at the ends of the X, the 6 in column 9 is satisfied either at r1c9 or r9c9 - not relevant at this stage which of the two. However that fact assists in revealing r7c9=9 only from which the rest follows.

IJ open the bubbly!!
su_doku

Posts: 30
Joined: 19 March 2005

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