The New Sudoku Players' Forum

by **Carcul** » Tue Dec 20, 2005 11:36 pm

In this post I present six exercises for all those who like to use nice loops or just want to try out their use and apply the principles of the bilocation-bivalue plot technique. The purpose of the exercises is the same: to solve each puzzle using only nice loops (and, of course, the more basic techniques up to X-Wings and Swordfishes, for example; XY-Wings and anything beyond that is “not allowed”). The six puzzles presented here have been already posted in this forum.

Exercise 1:

Code: Select all: . . . | . . . | . . . . 9 . | 8 . 5 | . 4 . . . 6 | . 7 . | 8 . . -------+-------+------ . 5 . | . . . | . 3 . . . 1 | . 8 . | 6 . . . 4 . | . . . | . 2 . -------+-------+------ . . 2 | . 6 . | 7 . . . 6 . | 1 . 9 | . 5 . . . . | . . . | . . .

This is an “easy” puzzle, useful for those who are making the “first steps” in the bilocation-bivalue plot technique. The solution can be reached easily.

Exercise 2:

Code: Select all: . . . | . 2 . | . 8 . 1 . 9 | . . 5 | 3 . . 7 . . | . . 4 | 1 . 5 -------+-------+------ . . . | 6 4 . | 5 . . 9 . . | . . . | . . 8 . . 3 | . 9 2 | . . . -------+-------+------ . . 2 | . . . | . . 1 . . 1 | 4 . . | 2 . 3 . 6 . | . 5 . | . . .

Another easy puzzle. As an additional exercise, the reader may want to try to solve this grid with a single advanced nice loop (after the basic steps).

Exercise 3:

Code: Select all: . 6 9 | 1 4 3 | 8 . 7 . . 7 | 9 . . | . . 4 4 . . | 7 . . | . 9 3 -------+-------+------ 9 . . | 8 5 7 | 3 6 1 7 . . | 2 1 6 | 9 4 5 6 1 5 | 3 9 4 | 2 7 8 -------+-------+------ . 7 . | 5 8 9 | 4 1 . 8 . . | 6 7 1 | 5 3 . . . . | 4 3 2 | 7 8 .

This one can be easily solved using uniqueness, but using the bilocation-bivalue plot is also "easy".

Exercise 4:

Code: Select all: 2 3 . | 5 4 . | 9 . 8 9 4 . | . . . | . . 3 1 8 . | 9 . . | . 4 . -------+-------+------- . 5 4 | . 1 . | 8 9 . . 9 3 | 8 . 4 | 5 . 1 8 2 1 | 7 9 5 | 3 6 4 -------+-------+------- 3 1 . | 4 . . | . 8 . 4 6 . | . . . | . . 9 5 7 . | 2 . . | 4 . 6 Menneske.no Very Hard #1751664

This one is a little harder but the solution is also straightforward.

Exercise 5:

Code: Select all: . . 1 | . 8 . | 6 . 4 . 3 7 | 6 . . | . . . 5 . . | . . . | . . . -------+-------+------ . . . | . . 5 | . . . . . 6 | . 1 . | 8 . . . . . | 4 . . | . . . -------+-------+------ . . . | . . . | . . 3 . . . | . . 7 | 5 2 . 8 . 2 | . 9 . | 7 . .

This puzzle is similar to the "third toughest puzzle", but it is somewhat easier. See the Note.

Exercise 6:

Code: Select all: 7 . . | 2 . . | . . 9 . . . | . 7 . | 2 . 6 . . 8 | 3 . . | . . . -------+-------+------ 3 . . | . 9 . | 5 . . . 4 . | . . . | . 3 . . . 1 | . 6 . | . . 7 -------+-------+------ . . . | . . 5 | 7 . . 4 . 3 | . 1 . | . . . 5 . . | . . 8 | . . 4

This puzzle was posted in this forum in the thread entitled “Super Tough Sudoku from Crazy Dad...would love just a nudge” (16th November). It is the hardest of the six (at least from my viewpoint) and it is possible to find a lot of loops in it. See the Note.

Note: The aim of the last two exercises is also to solve the grids using only nice loops: however, contrary to exercises 1-4, in exercises 5 and 6 the nice loops can be not only simple, but also strong, weak, triple, or nice loops including disjoint subset links (I use the expression “triple nice loop” to designate a triple implication chain ‘composed’ of three simple nice loops).

Have fun.

Carcul

by **Hud** » Tue Dec 20, 2005 11:51 pm

Carcul, I dubbed #3 into the Pappocom format and it wouldn't accept it. That's pretty common (I think) on puzzles requiring advanced techniques. I guess I'll try it on paper and get my ego totally destroyed.
By the way, I don't know if English is your mother tongue, but you express yourself very well.

by **Jeff** » Wed Dec 21, 2005 1:24 am

Carcul wrote:The aim of this last exercise is also to solve the puzzle using only nice loops: however, in this case, these nice loops can be not only simple, but also strong, weak, triple, or nice loops including conditional disjoint subset links (I use the expression “triple nice loop” to designate a triple implication chain ‘composed’ of three simple nice loops).

This is great. Could you give an example of a CDSL (conditional disjoint subset link)?

by **Jeff** » Wed Dec 21, 2005 4:10 am

Carcul,

I have completed excercise 1 using just a bilocation plot. I could post it (without solution) if anyone wants to see what my diagram looks like.

I am having a go at exercise 3 and only able to identify one simple nice loop so far. It is pretty tough.

by **Hud** » Wed Dec 21, 2005 5:20 am

Jeff, I have had a go at #3 also and think I'm in over my head. I did a couple basic moves and tried a swordfish on 7s but think it didn't work. I really need more swordfish work. I guess I'll go back to example 1 and really get humiliated lol.

by **Jeff** » Wed Dec 21, 2005 6:06 am

Hud, here are the candidate grids after all the basic moves.

Exercise 1

Code: Select all: *--------------------------------------------------------------------* | 1 8 45 | 2 349 6 | 359 7 39 | | 7 9 3 | 8 1 5 | 2 4 6 | | 45 2 6 | 349 7 34 | 8 1 359 | |----------------------+----------------------+----------------------| | 2 5 89 | 6 49 17 | 14 3 78 | | 3 7 1 | 45 8 2 | 6 9 45 | | 6 4 89 | 39 359 17 | 15 2 78 | |----------------------+----------------------+----------------------| | 459 13 2 | 345 6 34 | 7 8 1349 | | 8 6 7 | 1 234 9 | 34 5 234 | | 49 13 45 | 7 2345 8 | 349 6 12349 | *--------------------------------------------------------------------*

Exercise 2

Code: Select all: *--------------------------------------------------------------------* | 456 3 45 | 1 2 79 | 479 8 467 | | 1 48 9 | 78 678 5 | 3 467 2 | | 7 2 68 | 389 368 4 | 1 69 5 | |----------------------+----------------------+----------------------| | 2 1 78 | 6 4 78 | 5 3 9 | | 9 457 4567 | 357 1 37 | 467 2 8 | | 4568 4578 3 | 578 9 2 | 47 1 467 | |----------------------+----------------------+----------------------| | 458 45789 2 | 3789 378 36789 | 4678 4567 1 | | 58 5789 1 | 4 78 6789 | 2 567 3 | | 3 6 478 | 2 5 1 | 4789 479 47 | *--------------------------------------------------------------------*

Exercise 3

Code: Select all: *-----------------------------------------------------------* | 25 6 9 | 1 4 3 | 8 25 7 | | 1235 2358 7 | 9 26 58 | 16 25 4 | | 4 258 18 | 7 26 58 | 16 9 3 | |-------------------+-------------------+-------------------| | 9 24 24 | 8 5 7 | 3 6 1 | | 7 38 38 | 2 1 6 | 9 4 5 | | 6 1 5 | 3 9 4 | 2 7 8 | |-------------------+-------------------+-------------------| | 23 7 36 | 5 8 9 | 4 1 26 | | 8 249 24 | 6 7 1 | 5 3 29 | | 15 59 16 | 4 3 2 | 7 8 69 | *-----------------------------------------------------------*

Exercise 4

Code: Select all: *-----------------------------------------------------------* | 2 3 67 | 5 4 167 | 9 17 8 | | 9 4 567 | 16 2678 2678 | 1267 257 3 | | 1 8 567 | 9 2367 2367 | 267 4 257 | |-------------------+-------------------+-------------------| | 67 5 4 | 36 1 236 | 8 9 27 | | 67 9 3 | 8 26 4 | 5 27 1 | | 8 2 1 | 7 9 5 | 3 6 4 | |-------------------+-------------------+-------------------| | 3 1 29 | 4 567 679 | 27 8 257 | | 4 6 28 | 13 3578 378 | 127 2357 9 | | 5 7 89 | 2 38 1389 | 4 13 6 | *-----------------------------------------------------------*

Exercise 5

Code: Select all: *-----------------------------------------------------------------------------* | 29 29 1 | 57 8 3 | 6 57 4 | | 4 3 7 | 6 25 129 | 129 1589 12589 | | 5 6 8 | 1279 247 1249 | 1239 1379 1279 | |-------------------------+-------------------------+-------------------------| | 12379 124789 349 | 2789 2367 5 | 12349 134679 12679 | | 2379 2479 6 | 279 1 29 | 8 34579 2579 | | 12379 12789 5 | 4 2367 2689 | 1239 13679 12679 | |-------------------------+-------------------------+-------------------------| | 1679 1479 49 | 1258 2456 12468 | 149 14689 3 | | 1369 149 349 | 18 46 7 | 5 2 1689 | | 8 5 2 | 3 9 146 | 7 146 16 | *-----------------------------------------------------------------------------*

Exercise 6

Code: Select all: *--------------------------------------------------------------------* | 7 156 456 | 2 458 146 | 3 458 9 | | 19 3 459 | 14589 7 149 | 2 458 6 | | 269 269 8 | 3 45 69 | 14 7 15 | |----------------------+----------------------+----------------------| | 3 2678 267 | 1478 9 1247 | 5 1246 128 | | 2689 4 25679 | 1578 258 127 | 1689 3 128 | | 289 2589 1 | 458 6 3 | 49 249 7 | |----------------------+----------------------+----------------------| | 12689 12689 269 | 469 24 5 | 7 1269 3 | | 4 2679 3 | 679 1 279 | 689 2569 258 | | 5 12679 2679 | 679 3 8 | 169 1269 4 | *--------------------------------------------------------------------*

by **Carcul** » Wed Dec 21, 2005 10:23 am

Hi Hud.

Hud wrote:By the way, I don't know if English is your mother tongue, but you express yourself very well.

Thanks. In Portugal we all see a lot of movies speaked in English, and I guess that help.

I think sometimes I make errors, but the important is that you and the other users understand what I write. My mother tongue is Portuguese, and sometimes I need to have the English dictionary "at hand" to help me write these posts.
Have fun with these puzzles, because that is the most important.

Regards, Carcul

by **Carcul** » Wed Dec 21, 2005 10:35 am

Hi Jeff.

Jeff wrote:This is great. Could you give an example of a CDSL (conditional disjoint subset link)?

Sorry. My intention was to write "disjoint subset link", a situation where we have an almost locked set (ALS) in which there are 2 candidates "a" and "b" that appear each in just one cell of the ALS, and so we can consider the link =a|b=. I have already edited the original post.

Jeff wrote:I have completed excercise 1 using just a bilocation plot. I could post it (without solution) if anyone wants to see what my diagram looks like.

Good work. However, forgive me to ask you to not post your plot, because I would like that as much people as possible can reach the solution just by himselfs, without any influence from the plot or solution from others.

Jeff wrote:I am having a go at exercise 3 and only able to identify one simple nice loop so far. It is pretty tough.

But, how about Exercise 2?

Regards, Carcul.

by **Jeff** » Wed Dec 21, 2005 12:25 pm

Carcul wrote:But, how about Exercise 2?

I started with exercise 3 and went back to exercise 1 in despair. I haven't had a chance to try exercise 2 yet.

by **Carcul** » Wed Dec 21, 2005 4:48 pm

I have added two more exercises in the original post.

Carcul

by **Hud** » Wed Dec 21, 2005 10:13 pm

Jeff wrote:
Carcul wrote:But, how about Exercise 2?

I started with exercise 3 and went back to exercise 1 in despair. I haven't had a chance to try exercise 2 yet.

Jeff, I got the same candidate grid on puzzle 3 as you did. I still don't know if I did the swordfish correctly though. When I get time, I'll post my probably erroneous method.

Carcul, when I was in the army nearly 50 years ago, I had a friend who was a native of Brazil. As you know, they also speak Portugese which seemed similar to Spanish and a bit like French if I recall correctly.

by **Bob Hanson** » Thu Dec 22, 2005 1:39 am

Exercise #5

I'll be interested to see how people do this one.

Sudoku Assistant reports: W2MwP+ or (with almost-locked sets) AaW3MwP+

The P+ here implies we need hypothesis and proof (trial and error) with at
least hidden singles "look-ahead". Some people refer to this as "bifurcation
tabling." Mw is weakly-linked chain analysis; W2/W3 are X-wings/Swordfish,
and A/a is almost-locked set analysis.

Without the hypothesis/proof business, we get here without almost-locked set analysis:

Code: Select all: |---c1--|---c2--|---c3--||---c4--|---c5--|---c6--||---c7--|---c8--|---c9-- ----------------------------------------------------------------------------- r1 | 7 | 156 | 456 || 2 | 458 | 146 || 3 | 458 | 9 ---+-------+-------+-------||-------+-------+-------||-------+-------+------- r2 | 19 | 3 | 459 || 14589 | 7 | 149 || 2 | 458 | 6 ---+-------+-------+-------||-------+-------+-------||-------+-------+------- r3 | 269 | 269 | 8 || 3 | 45 | 69 || 14 | 7 | 15 ===========================||=======================||======================= r4 | 3 | 2678 | 267 || 1478 | 9 | 1247 || 5 | 1246 | 128 ---+-------+-------+-------||-------+-------+-------||-------+-------+------- r5 | 2689 | 4 | 25679 || 1578 | 258 | 127 || 1689 | 3 | 128 ---+-------+-------+-------||-------+-------+-------||-------+-------+------- r6 | 289 | 2589 | 1 || 458 | 6 | 3 || 49 | 249 | 7 ===========================||=======================||======================= r7 | 12689 | 12689 | 269 || 469 | 24 | 5 || 7 | 1269 | 3 ---+-------+-------+-------||-------+-------+-------||-------+-------+------- r8 | 4 | 2679 | 3 || 679 | 1 | 279 || 689 | 2569 | 258 ---+-------+-------+-------||-------+-------+-------||-------+-------+------- r9 | 5 | 12679 | 2679 || 679 | 3 | 8 || 169 | 1269 | 4 -----------------------------------------------------------------------------

and here, just a bit better, with almost-locked set analysis:

Code: Select all: |---c1--|---c2--|---c3--||---c4--|---c5--|---c6--||---c7--|---c8--|---c9-- ----------------------------------------------------------------------------- r1 | 7 | 156 | 456 || 2 | 458 | 16 || 3 | 458 | 9 ---+-------+-------+-------||-------+-------+-------||-------+-------+------- r2 | 19 | 3 | 45 || 14589 | 7 | 149 || 2 | 458 | 6 ---+-------+-------+-------||-------+-------+-------||-------+-------+------- r3 | 269 | 269 | 8 || 3 | 45 | 69 || 14 | 7 | 15 ===========================||=======================||======================= r4 | 3 | 2678 | 267 || 1478 | 9 | 1247 || 5 | 1246 | 128 ---+-------+-------+-------||-------+-------+-------||-------+-------+------- r5 | 2689 | 4 | 25679 || 1578 | 258 | 127 || 1689 | 3 | 128 ---+-------+-------+-------||-------+-------+-------||-------+-------+------- r6 | 289 | 2589 | 1 || 458 | 6 | 3 || 49 | 249 | 7 ===========================||=======================||======================= r7 | 12689 | 12689 | 269 || 469 | 24 | 5 || 7 | 1269 | 3 ---+-------+-------+-------||-------+-------+-------||-------+-------+------- r8 | 4 | 2679 | 3 || 679 | 1 | 279 || 689 | 2569 | 258 ---+-------+-------+-------||-------+-------+-------||-------+-------+------- r9 | 5 | 12679 | 2679 || 679 | 3 | 8 || 169 | 1269 | 4 -----------------------------------------------------------------------------

good luck!

by **Hud** » Thu Dec 22, 2005 5:42 am

Jeff, in reply to your candidate grid on puzzle 1, how did you eliminate the 5s at R1C9, R6C4, and R9C1? Pappocom rated it as a very hard but I appear to be stuck. I know I'm in over my head, but I guess this is the only way to learn.

by **Jeff** » Thu Dec 22, 2005 7:53 am

Due to a swordfish, Hud.

by **Carcul** » Thu Dec 22, 2005 12:18 pm

I have edited the original post (one more exercise added) for the last time.

Carcul

The New Sudoku Players' Forum

Nice Loops: some exercises

Nice Loops: some exercises

Re: Nice Loops: some exercises