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V Hard puzzles

 
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David



Joined: 02 Jun 2006
Posts: 58
Location: Bedford, UK

PostPosted: Sun Jul 23, 2006 1:08 pm    Post subject: V Hard puzzles Reply with quote

Over the past two months I have had no problems with a 'very hard', but struggled with some of the 'hard' puzzles (4 to be exact). I have come to the conclusion that I have the most difficulty when there are large number of candidates and hidden pairs etc are more difficult to spot. Conversely, it is very easy to spot an X wing or UR when most of the numbers have already been identified. I assume the software does not allow for these scenario's, but presumably could be ?
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Sun Jul 23, 2006 1:23 pm    Post subject: I'm not sure about the software ... Reply with quote

Hi, David!

I guess you're asking if the program that assigns difficulty ratings takes account of how many cells remain unresolved when a "hard" logic step is needed -- is that it? If so, I don't think it does. As I understand the explanations samgj has given already, the difficulty rating is based on the number of "choke points" in a puzzle -- three or more qualify it for the "very hard" rating.

Here's a suggestion about "hidden pairs" -- you can almost always find these without resorting to candidate lists for the unresolved cells. Too many extra pencil marks just make the puzzle confusing, anyway. The trick is to spot the pair elsewhere in the puzzle, and notice which cells in a box/column/row cannot possibly contain the pair -- when those two values can only fit in two spots, you've found a hidden pair. I can usually (not always!) do this without making any extra pencil marks. dcb
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David



Joined: 02 Jun 2006
Posts: 58
Location: Bedford, UK

PostPosted: Sun Jul 23, 2006 1:29 pm    Post subject: Reply with quote

Hi David

Many thanks for that, I will have a go using old puzzles from the archive.
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Sun Jul 23, 2006 8:10 pm    Post subject: Reply with quote

Let me add to dcb's comments:

When you find a pair from the candidate lists, stop for a while to figure out how you could have found the pair by looking at the solved cells. Soon, you will be finding pairs without pencil marks (PM's)!

Also, when you find a pair, have a quick look for a possible Unique Rectangle. This is an easy check; but, remember, a UR is in only two boxes!

Make minimal use of PM's. This is not a macho thing, it is because it is so difficult to keep all the PM's correct as you solve the puzzle. An extra incorrect candidate in a cell can be a real brick wall!

Once you have mastered finding pairs from the solved cells, you can then go the next step: Finding box / line interactions without PM's.

Keith
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samgj
Site Admin


Joined: 17 Jul 2005
Posts: 106
Location: Cambridge

PostPosted: Sun Jul 23, 2006 10:34 pm    Post subject: Re: I'm not sure about the software ... Reply with quote

David Bryant wrote:
As I understand the explanations samgj has given already, the difficulty rating is based on the number of "choke points" in a puzzle -- three or more qualify it for the "very hard" rating.


This is historically true, and draw/play still bases its judgement on this, but for the past couple of months I've subjectively filtered the uploaded very hard puzzles for a slight increase in difficulty.

Sam
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fanya



Joined: 24 Jul 2006
Posts: 8

PostPosted: Mon Jul 24, 2006 10:31 pm    Post subject: choke points Reply with quote

A couple of people have mentioned "choke points" for evalutating the difficulty of sudoku puzzles. Could someone explain what a choke point is? Or post a link to an explanation? Thanks.

Fanya
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Last edited by fanya on Mon Jan 31, 2011 6:38 pm; edited 1 time in total
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Mon Jul 24, 2006 11:32 pm    Post subject: choke points Reply with quote

I've never seen it defined, fanya, but from what samgj has said I gather that a "choke point" arises when there's only one logic step that can lead to the placement of another number in the puzzle.

Think of the various steps that are possible at the outset of the puzzle. There are usually several of these. But after making a number of moves, you'll (usually) reach a point where it's pretty hard to figure out what to do next, because there's only one logical step available. Depending on how skillful you are, and how familiar you are with this particular situation, you may find that one move (the way past the choke point) in a hurry. Or you may have to hunt for quite a while.

A puzzle that always has at least two ways to place another number is subjectively very easy. A puzzle that forces one to search for the only available move on several different occasions is subjectively much more difficult. dcb
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fanya



Joined: 24 Jul 2006
Posts: 8

PostPosted: Mon Jul 24, 2006 11:55 pm    Post subject: well that explains it then Reply with quote

Re: choke point

I've been playing Daily Sudoku since around April. And I've been noticing, for myself, that I can do all the puzzles with forward logic except the very hard ones. For those, I've had to guess, or what I have come to call, "double-entry guessing". This is where I chose a cell with just two possible numbers and continue in a forward logical way but with two sets of possibles in each cell which I visit from then on. Usually, this results in either a contradiction in one of the branches, or a cell filled in with the same number in both branches. At this point I stop the double-entry technique and fill in that number and go from there. Or if I never get to such a "same" cell, I just finish the branch which did not lead to a contradiction.

I've been able to do this with just the naked, and hidden tuple techniques, and the "row and column blocking and capture" (*not sure what the terminology for these are) techniques. It's only the very hard puzzles where I've had to guess. I have not perfected the x, xy-wing and unique rectangle techiques yet. I also find the forced choice technique hard to follow and recognize. I can usually do the "double-entry guessing" faster and I find it easier than the long-chains-of-logic techniques.

I will have to look out for this "choke point" idea now.

What I mean by "that explains things" is that Sunday's puzzle, 7/23/06, was the first very hard one for which I did not have to guess. I could do it all in a forward logic way. So I thought it might be misclassified. But since it's classified by the "choke point" method, I guess I should start to learn these other logic techniques so I can do even hard ones in a forward logical way.

Fanya
---------------
* I'll have to look up these sets of techniques and post the names. I'm not familiar enough with the terminology. And different sites use different terminology.


Fanya
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Last edited by fanya on Mon Jan 31, 2011 6:39 pm; edited 2 times in total
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fanya



Joined: 24 Jul 2006
Posts: 8

PostPosted: Tue Jul 25, 2006 1:06 am    Post subject: what I was calling row and column blocking and capture Reply with quote

Ok, what I was calling "row and column blocking and capture" is called locked candidates by SudoCue.net. They are also called "pointing pairs". I don't like the term "locked candidates" because it doesn't reflect the two different types of patterns illustrated by this technique: eliminating candidates outside a box in a given row or column, and eliminating candidates inside a box outside the taget row or column.

Fanya
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