US State Jigsaw

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US State Jigsaw

Postby motris » Sat Jun 10, 2006 3:33 am

So in solving r.e.s.'s irregular toroidal recently which you can find in this section of the forum, I took to "naming" some of the nonets, including one after New Hampshire, even though there is a better way to draw NH in 9 squares than the nonet I was so naming. After a poster on another site (jokingly?) referred to another nonet in the puzzle as Illinois, I came to wondering if I could construct a jigsaw sudoku out of state-shaped pieces and ended up with the one below. While a little gimmicky, I thought I'd share this puzzle with you all. It has a couple tricky steps but can be completely solved using logic alone. Enjoy!:D

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Postby Pyrrhon » Sat Jun 10, 2006 4:46 am

Thank you for the puzzle. In djape's forum there was a Australia zero killer and I saw an union jack. I'm wondering that national themes seems always related to english speeking countries.

To solve the puzzle I used neither leftovers nor paired pointing pairs (but jigsaw-line and line-jigsaw interaction). I found a x-wing and a skyscraper at my path. The rest were hidden and naked singles or pairs.

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Postby r.e.s. » Tue Jun 13, 2006 9:43 pm

Nice puzzle, motris. I finally got around to looking at it -- was having too much fun with the toroidals.:) Because LoL is extremely effective & (imo) especially simple to apply in plain jigsaw sudokus, I thought I would post one possible solution-path that uses it ...

[2007-04-05: Updated link address.]

This will paste directly into SumoCue:


The picture shows the "sticking point" after basic moves (hidden singles, line-tile interactions, and naked pairs), with an obvious coding for the letters. Since the blue cells must contain the same set of digits as the red ones, and the latter contain a 1 (in the naked pair 19-19), it follows that one of the candidate 1's in blue must be correct -- eliminating the other candidate 1's in that row.

EDIT: I posted the above thinking that only simple moves remain after the LoL move, but that's evidently not the case. I've left the LoL move in the picture for illustration, but the indicated chain on 3's (a "skyscraper" -- maybe the one Pyrrhon had in mind -- also described below by motris) solves the puzzle at this point by eliminating the 3 in r5c3.
Last edited by r.e.s. on Thu Apr 05, 2007 10:00 pm, edited 4 times in total.
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Postby motris » Tue Jun 13, 2006 11:21 pm

Thank you both for your comments. My goal was to make an aesthetically pleasing puzzle that fit the constraints I had in mind going in (use states and their initials exclusively as the shapes/givens); that it turned out to be of a reasonable difficulty was a bonus.

I've never even heard of the skyscraper technique so your comment pyrrhon gives me a chance to learn something new.

When I got to a similar sticking point, r.e.s., I noticed the chain of locked 1's and 3's (or K's and W's) and saw by a parity argument that R4C2 and R5C6 must be opposite digits and therefore both serve to eliminate all but the 9 in R5C3. Your posts though are definitely suggesting that LoL is a technique I underuse and can experiment more with. While I'll see "simple" cases (like say Long Island on NY and the tip of VA) and larger sets that use parts of single rows/columns/shapes as the leftovers pretty routinely, the kind of situation you've drawn is one step beyond where I seem to ever take LoL.
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Postby r.e.s. » Wed Jun 14, 2006 1:27 am

Oops, sorry! My mistake ... after that LoL move, the remaining moves are not all basic ones (afaics).

Pyrrhon, no doubt the "skyscraper" you had in mind is just motris' "parity argument" -- a simple chain in only one digit-value with two conjugate links in alternation. That does seem to be the neatest way to go, e.g. eliminating the 3 in r5c3. (As motris said, the 1 in r5c3 can be eliminated the same way, but it also gets eliminated by further basic moves otherwise.)

I'll edit my post above accordingly, and will put the skyscraper/chain in the picture. (For illustration I'll leave the LoL move in the picture, though it's clearly not the best one to make at this point.)
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Postby Pyrrhon » Wed Jun 14, 2006 5:12 am


The skyscraper is a special case of a turbot fish. If a turbot fish is no x-wing and has only two strong links then they are named as follows (at least in this forum):

A skyscraper is the special case of a turbot fish with both strong links in parallel lines.

If one strong link is in an row and the other one in a column it is called a 2-string kite.

If one strong link is in a line and the other one in a box/jigsaw (but not in a line) it is called a Fish pattern.

I'm not sure if there are names for turbot fishs with 3 or 4 strong links and for other cases in sudoku variants. (turbot fish with 2 strong links in diagonals in a sudoku x would be a nice theme for a variant puzzle, other cases we could get in extra regions sudoku variants, killer sudoku, sudoku with digit repitition).

In the picture above we have a turbot fish with 3 strong links.

I have not noted the way but only the techniques I used and so I can't say which skyscraper it was.

Last edited by Pyrrhon on Wed Jun 14, 2006 1:23 am, edited 1 time in total.
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Postby motris » Wed Jun 14, 2006 5:19 am

I see once again that my lack of familiarity with the names of the techniques does not prevent me from using them. Apparently, I've been fishing for awhile and just have not known to call the step a skyscraper or other kind of turbot fish.

I should comment that my "sticking point" picture is a little further in than your picture r.e.s. which helped me see the importance of the square I did the skyscraper-like step to. I saw the locked pair 45 in r5c12 which then eliminates the 9 in c2 in that box which eliminates the 9 in r2c3 which lets you solve all of the WV piece and more of the AL piece. You still are left though with the same basic sticking point to proceed further with the puzzle and I have not yet found another route forward from there although I may revisit it at some point. Still, while perhaps LoL is not enough here, your solution of your first irregular torroidal was really clean with it and so, as I said, I will be looking to explore its use more in the future.
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Postby Pyrrhon » Wed Jun 14, 2006 6:34 am

I solved the puzzle again. Here my walk through (I use the same numbers as r.e.s. Now I got a Fish pattern.

1st step: Hidden Singles 4 in R1, 1 in R2, 7 in R6, 7 in R8, 2 in C9, 7 in AL, 9 in VA, 7 in R2, 9 in R8, 2 in C1, 7 in WV, 7 in R3, 9 in C4, 9 in C5, 2 in FL, 4 in FL, 2 in R3, 2 in C5, 4 in NV,

2nd step: Naked Pair 3 and 5 in R6, Naked Pair 3 and 5 in C4 (R5C4=8, R9C4=2), Hidden Singles 4 and 8 in R9, 8 in C5,

3rd step: Naked Pair 5 and 6 in C6, Naked Pair 1 and 3 in C6 (R7C8=8), Hidden Single 8 in C9

4th step: Naked Pair 1 and 3 in C7, Line-Jigsaw interaction with candidate 9 between R1 and WY deletes candidate 9 at R2C7, Hidden Single 9 in C7, Jigsaw-Line interaction with 5 between AL and R5 deletes 5 at R5C5 R5C9, with 6 between NV and C9 deletes 6 at R1C9 R9C9, between NY and C5 deletes 6 at R8C5

5th step: Hidden Pair with 4 and 5 in R5 deletes in R5C1 R5C2, Hidden Single 9 in C2, R2C3=6, R2C1=5, R2C7=8, R1C1=3, R5C1=4, R3C2=8, R5C2=5, R8C1=6, Hidden Single 4 in R8, Naked Pair 1 3 in C7 and R7

6th step: X-Wing with strong links in R4 R6 and weak links in AL and NV deletes 1 in R5C3 R5C9, Turbot Fish (Fish Pattern) with strong links R4C2-R4C7 in R4 and R7C2-R6C4 in NY deletes candidate 3 at R6C8, R6C8=5.

And the rest is obvious.

You can apply the x-wing and the turbot fish in the picture of r.e.s. too, but these are different from the LOL and turbot fish conclusions r.e.s has painted into the diagram.

PS: Okay, I've found a skyscraper again. Take the picture of r.e.s: Strong links R6C4-R6C8 in R6, and R7C2-R7C7 in R7 with respect to candidate 3 deletes this candidate in R4C7. So is R4C7=1.
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Postby Smythe Dakota » Fri Jun 16, 2006 2:19 am

Well, just to change the subject (slightly):

I've got to be REALLY impressed, first of all, that you even found 9 state names which used exactly 9 different letters (an average of twice each). Then, second, you managed to fit the 9 shapes for these states into a 9x9 square (although, obviously, you were able to take a few liberties here and there). Finally, third, you had to fit the nine letter pairs into the nine pieces -- each pair horizontally adjacent, no less -- in such a way as to create a valid Sudoku with a unique solution.

That's got to be an impressive accomplishment. Congratulations!

Bill Smythe
Smythe Dakota
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Postby PaulIQ164 » Thu Jun 22, 2006 11:28 pm

The construction of this sudoku is clearly the greatest achievement in the history of the puzzle.
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