## Sticking to one trick

Advanced methods and approaches for solving Sudoku puzzles

### Sticking to one trick

Just by way of a change I wanted to see if a grid could be solved using X-wings ONLY. Today's Times 'fiendish' proved exceptionally easy to crack using just three or four x-wings and the resulting hidden / open singles. - these were the ONLY tactics used - no pairs / triples etc. This begs the question - could ANY valid grid be solved solely by the application of x-wings?

stuartn

stuartn

Posts: 211
Joined: 18 June 2005

Interesting. I didn't find any X-wings in today's 'Fiendish' at all. This brings to mind something which occurred to me some time ago: namely that through judicious use of candidate placement it is occasionally possible to complete a puzzle through the simpler pairs/triple/etc. methods, rather than have to resort to X-wings and the like.

I'm probably not explaining myself very well and I apologise for using the word 'resort' in the last line, especially with all its despairing overtones. I lurve X-wings and find them as useful as anybody else, it's just that, rather than bombard a puzzle with every possible candidate from the very beginning, and then searching for X-wings and the like, it is frequently possible, even in the more taxing sudoku, to think along the lines of "Oh, of course, there can't be any 2's there because...blah..blah.." and without knowing it, you've actually just destroyed an X-wing which may have been exceedingly useful, but which, down the current pathway, turns out not to be needed. What's better - fewer steps or simpler steps? Let's have a heated debate!

Good point there stuartn: are there any all-powerful (or at least, semi-omnipotent) constructs which will slice, machete-like, through all but the most difficult puzzles? (I use the word 'construct' because, as has been pointed out before, one could say "Why yes, T & I will always work, it'll just take longer". I know, but let's not have that argument again, eh?)

Finally, a second, much more difficult question: is it possible, either through experience or the puzzle's clue placements to know which is the best construct to use at a specific point in a particular puzzle? If so, can this awareness be taught? Y'see, rather than invent clever techniques, I like to make people cleverer.

I just had my hair cut.
Karyobin

Posts: 396
Joined: 18 June 2005

Where possible, a puzzle should be solved without any filtering. Imagine when you are doing it directly on the newspaper diuring your lunch break.

I think you should do as much as possible without having to use x-wing at all.
Jeff

Posts: 708
Joined: 01 August 2005

Absolutely agree Jeff - but as an excercise to see what the limits of a technique were it was useful. If you've got a foolproof way of identifying doubles then its a VERY simple solving technique on par with simple elimination.

I started with the xw 6's @ r4c46 and r9,46 then another with the 9's @ r5,c28 and r6c28 . Then promoted the 6's @r1c9, r5c3 and r8c1. After this another xw of 2's @ r2c89 and r8,89 and promotion of the 2's @r4c1 and r5c7, then a last xw of 8's at r3c13 and r7,13. After that basic elimination got me there.

Of course I did the BASIC elimination of candidates as I went along aswell (lines, rows, blocks only - no doubles, triples or anything like that)

stuartn
Last edited by stuartn on Thu Aug 18, 2005 8:31 am, edited 1 time in total.
stuartn

Posts: 211
Joined: 18 June 2005

Jeff: I assume the 'without filtering' approach stems from a purity ideal, and by and large I whole-heartedly agree with you. I must admit though, mental development interests me as much as purity and as such I have no problem with filtering, provided I can hold the shape of the filter in my mind all at once.
Karyobin

Posts: 396
Joined: 18 June 2005

Karyobin wrote:

What's better - fewer steps or simpler steps?

I would venture 'more elegant steps.

stuartn

stuartn

Posts: 211
Joined: 18 June 2005

I did today's fiendish without much clever thinking beyond one use of the tactic whereby you have three cells each with the same two candidates in three-quarters of an X-Wing pattern, and from that deduce that the remaining cell can't hold either of those two candidates (as there'd be forced to be multiple solutions otherwise). I'd guess, therefore, that this puzzle was 'special', and you might not have as much luck trying this tactic with other fiendishes - I could be very wrong, of course.

I, of course, actually do do the puzzles in the newspaper, so I have to manage without filtering, but it's interesting how the puzzles play out when you can use different tactics.
PaulIQ164

Posts: 533
Joined: 16 July 2005

And that, of course Paul is the object of this august organ ! To share and broaden knowledge of the subject and to encourage deeper thought.

back to work now.

stuartn
stuartn

Posts: 211
Joined: 18 June 2005

Although I saw plenty of X-Wings in this puzzle, it was easier for me not to use them, because I was attempting to do it without pencilmarks, and the possible candidates for each cell would have been too difficult to keep track of if I had implimented the X-Wings that I saw.

Also, this puzzle had many more possible X-Wings than most Fiendishes do, so I'm not sure that it would be possible to solve every puzzle only using X-Wings and singles.

(Unfortunately, I had to put a few pencilmarks in because my brain missed the quad in column 9.)

G
george-no1

Posts: 150
Joined: 20 May 2005

Tried the same tactic with todays fiendish and needless to say - it failed. But it did get jolly close. I had to use a double at the end to give me the last few 'hidden' single promotions.

stuartn
stuartn

Posts: 211
Joined: 18 June 2005

I did today's Fiendish by nothing other than sitting and thinking. 's good to practice being clever occasionally. Sometimes I think we forget to see the wood for the trees.

Like Bruce said:

It is like a finger pointing to the moon. Don't concentrate on the finger or you will miss all the heavenly glory.
Karyobin

Posts: 396
Joined: 18 June 2005

Karyobin wrote:I did today's Fiendish by nothing other than sitting and thinking. 's good to practice being clever occasionally. Sometimes I think we forget to see the wood for the trees.

Ah, Karyobin, amongst your many wise pronouncements, this is the wisest.

- Wayne
Pappocom

Posts: 599
Joined: 05 March 2005

Pappocom wrote:
Karyobin wrote:I did today's Fiendish by nothing other than sitting and thinking. 's good to practice being clever occasionally. Sometimes I think we forget to see the wood for the trees.

Ah, Karyobin, amongst your many wise pronouncements, this is the wisest.

- Wayne

stuart
stuartn

Posts: 211
Joined: 18 June 2005

### re: The Times (2005.Aug.18) -- #308 -- Fiendish

The Times (2005.Aug.18) wrote:
Code: Select all
` . 3 . | . . . | . 8 .  . . 1 | 4 . 8 | 9 . .  . 2 . | . 6 . | . 7 . -------+-------+------ . . 3 | . 9 . | 8 . .  . . . | 8 . 1 | . . .  . . 5 | . 2 . | 6 . . -------+-------+------ . 5 . | . 4 . | . 6 .  . . 4 | 5 . 9 | 7 . .  . 7 . | . . . | . 1 . `

stuartn wrote:I wanted to see if a grid could be solved using X-wings ONLY.

Today's Times 'fiendish' proved exceptionally easy to crack
using just three or four x-wings and the resulting hidden / open singles.

these were the ONLY tactics used - no pairs / triples etc.

i saw 4 solution-paths ( different but quite similar ) --
• one "hidden" duo ( {4,5} in b9 or in r9 )
• one "naked" duo ( {r7c7,r8c8} in b9 )
• one line-to-box exclusion ( 2 r8\b9 )
• one X-wing ( 2 r28\c89 )

Pat

Posts: 3657
Joined: 18 July 2005

2005?!

Christ, what happened here - have you been doing this one for two years?
Karyobin

Posts: 396
Joined: 18 June 2005

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