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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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 Posted: Wed Dec 12, 2007 3:13 am Post subject: hard book puzzle |
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| Code: | 9 . . | . . 7 | . . .
. . . | . . 4 | . 1 .
. . 3 | . 8 6 | . . 5
------+-------+------
6 . . | . . . | 4 . .
. 7 2 | . . . | 3 6 .
. . 4 | . . . | . . 9
------+-------+------
4 . . | 5 9 . | 7 . .
. 8 . | 2 . . | . . .
. . . | 6 . . | . . 3 |
I am posting this puzzle because I think it's ridiculous that this level of difficulty is in a book with 3 1/2" x 3 1/2" 9x9 grids.
AND !!
the book has no literature included on any solving techniques except what a sudoku is and the rules that apply. ha !!
the book is broken down into 5 sections, each section gets increasingly harder. the book claims that by the time you end the book, you will be a sudoku expert.
publisher: Sterling
Author: Frank Longo
Title: Easy to Hard Mensa Sudoku
the above grid is puzzle #505 <-------------------
anyone follow me on this?
Norm
ps, i am not praising or smashing this book, I just wanted to get my opinion out. I actually have the book, I use to work for a book company, which led to my severely dependent sudoku addiction. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Wed Dec 12, 2007 6:08 am Post subject: |
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maybe the publishers thought that mentioning Mensa would be "fair warning" enough?
Long as it does not claim to be a textbook, a collection of challenges is what most people probably look for when purchasing a collection of puzzles (be it crossword or sudoku).
It was the casual encounter of "unsolvable" puzzles at my (then) level (which was naked pairs and hidden singles, mind you, and unsolvable meant the puzzle needed box/line interactions) that got me looking deeper into sudoku.
And that's not a bad thing, in my opinion. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Dec 12, 2007 6:13 am Post subject: |
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nataraj,
right, so the unobtained solution ( at the time ) led you to......
not using those squares they provide??? right??
crosswords have nothing on sudoku |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Wed Dec 12, 2007 3:31 pm Post subject: |
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| storm_norm wrote: |
right, so the unobtained solution ( at the time ) led you to......
not using those squares they provide??? right??
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Norm,
I'll take your question at face value.
a) I am still using the squares they provide. The local paper's puzzles are exactly 9x9 cm (which is approx. 3.54 in), I solve one sudoku every day, the difficulty varies but usually doesn't exceed the need for box/line interactions, sometimes the odd xwing thrown in. I do them while having breakfast with half an ear on the 6 o'clock news and it usually takes 14-19 minutes to complete one of these. The size is fine. I get my PMs in all right.
For comparison, I do this site's very hards in the evening or later in the morning (if I am lucky and the work on my morning mail is finished before 7:30 and I can slip in a quiet 25 minutes or so of sudoku at the office). I never time these vh's, but they normally take considerably more time (30-50 minutes) and need a lot more concentration. The size of the squares is similar - 9,5x9,5 cm (3.74 in), but I really appreciate that little extra space. (Thanks, dailysudoku.com. Whoever did the user interface design did a real good job!)
All in all - size 3,5 doesn't sound too terrible.
b)the squares they provide. Well I think we're back to talking about grading, difficulty, levels etc. here.
When the sudoku craze first hit a few years ago, I took one long look at it and said to myself: "Now, isn't that obvious? Just find the numbers that hadn't been used in a row, column or square and you got your solution. This is too trivial ...". Solved one (easy) and that was it. No more.
On vacation in Greece we always took along various puzzle books and my daughter and myself solved most of the puzzles in the book together. In one of those, there was a page of sudoku and out of pure boredom I started solving some of them on my own (can't do sudoku together, do you agree?). I discovered a method for finding hidden singles and I discovered the principle behind naked pairs there on the beach. And I found out there was much more intellectual challenge in sudoku than meets the eye at first glance. Not to solve sudoku like a computer but to solve sudoku as a human. that was very nice and I started solving sudokus in newspapers (mostly on planes, far as I recall)
My reaction to the first puzzle I could not solve (at that time, graded "extremely hard"!) by my homegrown means , was to use bifurcation and forcing chains (which is what we did back in college when looking for proofs in algebra 101...) and ... I was very frustrated. Not easy to do with pencil and paper, very shaky results.
What does a smart guy do when his own efforts don't yield immediate results? Right, google it.
And I found a wealth of techniques, plus ... a lot of puzzles to challenge my expanding skills. Like this site. Like many others.
c) Let me add a personal view about what I expect from sudoku books/sites.
challenges - challenges - challenges.
I hate to be treated like a six year old - this is the method. Now use the method. This is how x wings work. Here are the puzzles that need x wings.
This is how xy wings work. These puzzles need xy-wings.
You get my drift.
------
I am in no way affiliated with the publisher or the author of the book in question. And there might be a lot of reasons that got you mad. But the simple facts that it's got a real hard puzzle in it and the squares are 3 1/2 x 3 1/2 for me does not sound "ridiculous".  |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Dec 12, 2007 5:01 pm Post subject: |
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Grids 3.5" square size are adequate for me. The blanks I use, the printed ones from here or Brain Bashers are all that size or a fraction bigger. It holds all my PMs and is good for printing two on a page (plus I use both sides for four on a sheet).
Awhile back I wrote about a book I tried. It was a MENSA book called "Absolutely Nasty Sudokus" and came in Levels 1,2, 3 and 4. I tried the 3 and the puzzles were too easy. I would've taken a shot at the 4, but haven't seen it since. At any rate, I returned that one i bought. |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Wed Dec 12, 2007 9:00 pm Post subject: Hard book |
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Small grids are annoying, but posssible.
This puzzle seems impossible.
I found an xy-chain which eliminates a 1, to no further avail,
and a w-wing which eliminates nothing.
Help!
Earl |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Dec 12, 2007 9:32 pm Post subject: |
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thanx for the feedback guys.
I just wanted to hear some other opinions. obviously I would love to see larger grids especially for harder puzzles. I just keep wondering why the grid is the same size in most books or newspapers? who was playing devine almighty and said, " sudoku puzzles will be this size?". its just one of those research questions that is interesting to me.
anyways, back to the puzzle:
| Code: | 9 2456 56 | 1 25 7 | 8 3 46
278 256 5678 | 3 25 4 | 9 1 67
17 14 3 | 9 8 6 | 2 47 5
---------------------+----------------------+-------------------
6 19 189 | 78 3 25 | 4 257 127
5 7 2 | 4 1 9 | 3 6 8
138 13 4 | 78 6 25 | 15 257 9
---------------------+----------------------+-------------------
4 1236 4 | 5 9 138 | 7 28 12
137 8 59 | 2 47 13 | 6 59 14
127 1259 1579 | 6 47 18 | 15 24589 3 |
UR next? {2,5} in r46c68. so this is a type 2 if my research is correct because the 7's in column 8 can't leave the cells they are in. that means any other 7 they can see can be zapped !!
now my question is. this UR is useless if you can't eliminate anything, correct?? |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Wed Dec 12, 2007 9:33 pm Post subject: |
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I believe this is where basics take us:
| Code: |
+--------------------------+--------------------------+--------------------------+
| 9 2456 56 | 1 25 7 | 8 3 46 |
| 278 256 5678 | 3 25 4 | 9 1 67 |
| 17 14 3 | 9 8 6 | 2 47 5 |
+--------------------------+--------------------------+--------------------------+
| 6 19 189 | 78 3 25 | 4 257 127 |
| 5 7 2 | 4 1 9 | 3 6 8 |
| 138 13 4 | 78 6 25 | 15 257 9 |
+--------------------------+--------------------------+--------------------------+
| 4 1236 16 | 5 9 138 | 7 28 12 |
| 137 8 59 | 2 47 13 | 6 59 14 |
| 127 1259 1579 | 6 47 18 | 15 24589 3 |
+--------------------------+--------------------------+--------------------------+
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There is an xyz-wing (2,5,6) removes 5 from r2c3
And an xy-chain '16'(73)='65'(13)='59'(83)='95'(88)='51'(97) that removes 1 from cells r7c9 r9c1 r9c2 r9c3.
Or, one could exploit that DP 25 in c68 makes r3c8=4, which solves the puzzle in one step ... |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Dec 12, 2007 9:37 pm Post subject: |
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| I wonder how many times it happens that two people are posting at once?? |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Wed Dec 12, 2007 9:39 pm Post subject: |
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Ah, Norm, seems we posted at the same time.
I wanted to ask that question a while ago but got more involved in the other aspects of the story, but here goes:
why would you prefer larger grids? I'm not talking by a small amount like I said I love doing the daily sudokus from this site with the slightly larger grid. But no more than that.
Larger sizes prevent me from seeing the whole grid (whole row, column), the "total" picture. Plus, I can't think of any more things to put into the cells. A few PMs that's all.
Curious to find out ... |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Dec 13, 2007 2:58 am Post subject: |
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Let me introduce the idea of an M-link.
After the XYZ-wing, if you don't want to use the UR, you are here:
| Code: | +-------------------+-------------------+--------------------+
| 9 2456 56 | 1 25 7 | 8 3 46 |
| 278 256 678 | 3 25 4 | 9 1 67 |
| 17 14 3 | 9 8 6 | 2 47@ 5 |
+-------------------+-------------------+--------------------+
| 6 19 189 | 78 3 25 | 4 257 127 |
| 5 7 2 | 4 1 9 | 3 6 8 |
| 138 13 4 | 78 6 25 | 15 257 9 |
+-------------------+-------------------+--------------------+
| 4 1236 16 | 5 9 138 | 7 28 12 |
| 137 8 59 | 2 47@ 13 | 6 59 14 |
| 127 1259 1579 | 6 47% 18 | 15 24589% 3 |
+-------------------+-------------------+--------------------+
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The cells <47> @ are a W-link on <7>, connected by the strong link on <4> % in R9. One or both of A is <7>, any cell that sees both cannot be <7>.
This does not make any eliminations, even if you consider extending the wing by coloring on <7>.
But, consider this:
| Code: | +-------------------+-------------------+-------------------+
| 9 2456 56 | 1 25 7 | 8 3 46 |
| 278 256 678 | 3 25 4 | 9 1 67 |
| 17 14 3 | 9 8 6 | 2 47# 5 |
+-------------------+-------------------+--------------------+
| 6 19 189 | 78 3 25 | 4 257 127 |
| 5 7 2 | 4 1 9 | 3 6 8 |
| 138 13 4 | 78 6 25 | 15 257 9 |
+-------------------+-------------------+--------------------+
| 4 1236 16 | 5 9 138 | 7 28 12 |
| 137 8 59 | 2 47 13 | 6 59 14 |
| 127 1259 1579 | 6 47# 18 | 15 24589% 3 |
+-------------------+-------------------+--------------------+
|
The two cells # are connected via % by strong links on <4>. Either BOTH are <4>, or BOTH are <7>.
Now, lets look at extending the link by coloring on <7>:
| Code: | +-------------------+-------------------+-------------------+
| 9 2456 56 | 1 25 7 | 8 3 46 |
| 2-78 256 678 | 3 25 4 | 9 1 67a |
| 17 14 3 | 9 8 6 | 2 47A 5 |
+-------------------+-------------------+-------------------+
| 6 19 189 | 78 3 25 | 4 257 127 |
| 5 7 2 | 4 1 9 | 3 6 8 |
| 138 13 4 | 78 6 25 | 15 257 9 |
+-------------------+-------------------+-------------------+
| 4 1236 16 | 5 9 138 | 7 28 12 |
| 137A 8 59 | 2 47a 13 | 6 59 14 |
| 127 1259 1579 | 6 47A 18 | 15 24589 3 |
+-------------------+-------------------+-------------------+
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In B3 there is a link to R2C9.
In R98 there is a link to R8C5 and to R8C1.
We can eliminate <7> in any cell that sees both A and a. In particular, R2C1 is not <7>.
This is simply another way to recognize a pattern involving two cells with the same two candidates that are not a pair. If you can't make a W-wing, see if you can connect them with two strong links on one candidate.
M-wing?
M is an upside down W.
This is perhaps the simplest example of Medusa coloring.
(This is not the greatest example, but the puzzle was posted. Also, it has the W-wing. And, I fully appreciate there are other ways to look at and explain this.)
Best wishes,
Keith |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Thu Dec 13, 2007 12:43 pm Post subject: |
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| keith wrote: | | If you can't make a W-wing, see if you can connect them with two strong links on one candidate. |
Or both:
Puzzle by TTHsieh
| Code: | +-------+-------+-------+
| . 1 . | . 2 . | 3 . . |
| . . 4 | . . 3 | . 5 . |
| . 2 . | . . . | . . 6 |
+-------+-------+-------+
| . . 7 | 8 . . | . 4 . |
| . . . | 1 . . | . . 5 |
| . 8 . | . 9 5 | . . . |
+-------+-------+-------+
| 3 . . | . . 7 | . 9 . |
| . . . | 6 . . | 1 . 7 |
| . . 6 | . . . | . . . |
+-------+-------+-------+
*-------------------------------------------------------*
|@56789 1 58 | 4579 2 #46 | 3 78 89 |
|-6789 679 4 | 79 168 3 | 289 5 1289 |
| 5789 2 3 | 579 158 189 | 4 178 6 |
|-----------------+------------------+------------------|
| 15 356 7 | 8 36 26 | 29 4 1239 |
|#46 3-46 9 | 1 7 @246 | 28 2368 5 |
| 14-6 8 2 | 34 9 5 | 7 16 13 |
|-----------------+------------------+------------------|
| 3 45 1 | 25 458 7 | 6 9 248 |
| 24589 459 58 | 6 3458 89 | 1 238 7 |
| 24789 479 6 | 239 1348 189 | 5 238 2348 |
*-------------------------------------------------------*
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The strong links for 6 in row 1 and 4 in col 6 make the 46 cells "both 4 or both 6". At the same time they transport 6 to r1c1 and 4 to r5c6. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Thu Dec 13, 2007 3:54 pm Post subject: |
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Keith,
I see those {47}s as a Remote Naked Pair (no new name necessary). We have loosely defined a W-Wing as a matching remote pair that each "sees" the opposite ends of a strong link on one of their digits, resulting in them being "pincers" for the other digit. Usually, one or both of those "seeing" links will be weak. However, if both of the bivalue cells see the external strong link via strong links (and if all of the involved strong links are conjugate links as in this case), then they are a Remote Naked Pair and not just a W-Wing.
Ravel,
You have shown an AIC Loop. It is like an XY Loop (or other ALS Loop) but uses strong links within a house in two places in the chain (instead of the strong links within bivalue/ALS cells). In Eureka notation:
(4=6)r5c1-(6)r1c1=(6-4)r1c6=(4)r5c6-(4=6)r5c1-etc.
Because it is a continuous loop, all of the links become strong (conjugate) links and eliminate any peer candidates. So, the <6>s at r51c1 eliminate <6>s, r1c6 would have become a bivalue had there been any other candidates in it (it needn't be a bivalue cell for this situation to work), and the <4>s at r5c16 eliminate <4>s... as you have shown.
In plain language, the loop can be described as:
In one direction...
r5c1<>4 => r5c1=6 => r1c1<>6 => r1c6=6 => r1c6<>4 => r5c6=4 => r5c1<>4, etc.
In the other direction...
r5c1<>6 => r5c1=4 => r5c6<>4 => r1c6=4 => r1c6<>6 => r1c1=6 => r5c1<>6, etc.
Since all the cell values in one direction "flip" in the other direction, the links all become strong links.
I believe it is more beneficial to be able to see it as a loop than as transported pincers, even though that way of seeing it gets the job done in this case.
[Edit for typo] |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Dec 13, 2007 10:02 pm Post subject: |
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| Asellus wrote: | Keith,
I see those {47}s as a Remote Naked Pair (no new name necessary). We have loosely defined a W-Wing as a matching remote pair that each "sees" the opposite ends of a strong link on one of their digits, resulting in them being "pincers" for the other digit. Usually, one or both of those "seeing" links will be weak. However, if both of the bivalue cells see the external strong link via strong links (and if all of the involved strong links are conjugate links as in this case), then they are a Remote Naked Pair and not just a W-Wing. |
Asellus,
This is a little different. If - is a weak link and = a strong link then
W-link: WX-X=X-WX has W as pincers.
Remote pair: XY=X=X=XY has both X and Y as pincers. This remote pair is usually described as the more restrictive XY=XY=XY=XY.
M-link: XM=X=XM=M has M as pincers.
http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2195
Keith |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Fri Dec 14, 2007 12:12 am Post subject: |
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Keith,
I was thinking of the {47}s marked @ (which are a remote naked pair) since those were the ones you first referenced in your post above. Later, you refer to the pair marked #; but I thought that was just by way of explaining your point about @. Your linked post makes it clear you mean the # pair.
I agree that it is perhaps the simplest application of Medusa. |
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