The Effortless Extremes thread

Everything about Sudoku that doesn't fit in one of the other sections

Postby RW » Thu Oct 05, 2006 4:52 pm

wapati wrote:And this one, submitted earlier?


I wasn't sure if you wanted to make it more minimal, as it is possible while retaining symmetry and the BUG, but if you want it fully symmetrical I can put it like that also.

RW
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Postby wapati » Thu Oct 05, 2006 5:27 pm

RW wrote:
wapati wrote:And this one, submitted earlier?


I wasn't sure if you wanted to make it more minimal, as it is possible while retaining symmetry and the BUG, but if you want it fully symmetrical I can put it like that also.

RW


Thanks RW, I like the full symmetry, it is rare enough!
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Postby daj95376 » Sat Oct 07, 2006 4:19 am

RW,

You have this puzzle under BUG+2, but it's also a UR Type 1 for <14>.
Code: Select all
3. Mike Barker
 *-----------*
 |.4.|36.|1..|
 |...|...|7..|
 |.8.|19.|..2|
 |---+---+---|
 |2.5|...|...|
 |...|...|3..|
 |...|2..|..6|
 |---+---+---|
 |61.|...|.98|
 |95.|.4.|...|
 |7..|6..|2..|
 *-----------*

You have this puzzle under BUG+2, but it's also an XYZ-Wing on [r1c9].
Code: Select all
6. Mike Barker
 *-----------*
 |2.9|...|7..|
 |.8.|.49|...|
 |...|...|...|
 |---+---+---|
 |..4|1..|.9.|
 |.63|9..|4..|
 |5.8|2..|...|
 |---+---+---|
 |.32|81.|...|
 |...|...|6.5|
 |...|43.|..1|
 *-----------*

You have this puzzle under Unique Rectangles, but there appears to be more than one.
Code: Select all
*)  UR Type 1 for <34>
#)  UR Type 4 for <79> -- eliminates 9 in [r47c7]
@)  UR Type 4 for <15> -- eliminates 1 in [r79c5]

5. Mike Barker
 *-----------*
 |.7.|5..|...|
 |4..|19.|...|
 |51.|...|.9.|
 |---+---+---|
 |.43|.2.|.1.|
 |..8|...|.26|
 |.2.|3..|..5|
 |---+---+---|
 |...|...|.8.|
 |...|7..|.51|
 |79.|...|..2|
 *-----------*

 *--------------------------------------------------------------------*
 | 8      7      9      | 5      34*    2      | 1      6      34*    |
 | 4      3      2      | 1      9      6      | 5      7      8      |
 | 5      1      6      | 48     3478-  3478   | 2      9      34*    |
 |----------------------+----------------------+----------------------|
 | 69     4      3      | 689    2      5      | 789-   1      79#    |
 | 19     5      8      | 49     147    147    | 3      2      6      |
 | 169    2      7      | 3      168    18     | 89     4      5      |
 |----------------------+----------------------+----------------------|
 | 3      6      15@    | 2      145-   149    | 479-   8      79#    |
 | 2      8      4      | 7      36     39     | 69     5      1      |
 | 7      9      15@    | 468    14568- 148    | 46     3      2      |
 *--------------------------------------------------------------------*

You have this puzzle under Unique Rectangles, but there appears to be more than one.
Code: Select all
*) UR Type 4 for <46> -- eliminates 6 in [r5c47]
#) UR Type 4 for <67> -- eliminates 6 in [r1c12]

14. Mike Barker:
 *-----------*
 |...|..2|..4|
 |..1|7..|8..|
 |.4.|.6.|.3.|
 |---+---+---|
 |4.6|...|..5|
 |3.7|...|.8.|
 |...|..9|...|
 |---+---+---|
 |..9|.18|..2|
 |1..|...|.5.|
 |.5.|..4|76.|
 *-----------*

 *--------------------------------------------------------------------*
 | 56789- 3678-  358    | 1389   3589   2      | 156    19     4      |
 | 2569   236    1      | 7      4      35     | 8      29     69     |
 | 2589   4      258    | 189    6      15     | 125    3      7      |
 |----------------------+----------------------+----------------------|
 | 4      1289   6      | 1238   2378   137    | 12     1279   5      |
 | 3      129    7      | 1246-  25     156    | 1246-  8      69     |
 | 258    128    258    | 46*    278    9      | 46*    127    3      |
 |----------------------+----------------------+----------------------|
 | 67#    67#    9      | 5      1      8      | 3      4      2      |
 | 1      23     4      | 236    237    367    | 9      5      8      |
 | 28     5      238    | 239    239    4      | 7      6      1      |
 *--------------------------------------------------------------------*
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Postby RW » Sat Oct 07, 2006 5:36 am

Daj, thank you for checking the list for these every now and then.

daj95376 wrote:RW,

You have this puzzle under BUG+2, but it's also a UR Type 1 for <14>.

Interesting, how did that get there?

daj95376 wrote:You have this puzzle under BUG+2, but it's also an XYZ-Wing on [r1c9].

Most BUGs will also be XYZ-wings, I don't really mind it being there.

daj95376 wrote:You have this puzzle under Unique Rectangles, but there appears to be more than one.

That's no problem, as long as it's enough to use one of them to solve the puzzle.

RW
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Unique Loop +1

Postby wapati » Sat Oct 07, 2006 9:42 am

URs are fun but common. Unique Loops are unusual, thus more fun!

Code: Select all
8 . . | . 4 . | 9 . .
9 . 2 | . 3 6 | . . .
5 . . | 8 . 1 | . . 3
---------------------
1 9 . | 4 . . | 6 5 .
. . . | . 6 . | . 9 1
. . . | . . 8 | 2 . .
---------------------
. . 8 | . . . | . 4 .
. 5 . | . . 2 | . . .
. . . | . . 4 | 5 3 2
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Postby RW » Sat Oct 07, 2006 11:35 am

wapati wrote:Unique Loops are unusual, thus more fun!


Nice puzzle. My first reaction was to use this very uncommon size 10 BUG-lite:

Code: Select all
 *--------------------------------------------------*
 | 8   *13+7*13   | 2    4    57   | 9    16   567  |
 | 9    14   2    | 57   3    6    | 148  18   57   |
 | 5    47   6    | 8    9    1    | 47   2    3    |
 |----------------+----------------+----------------|
 | 1    9    7    | 4    2    3    | 6    5    8    |
 | 2    8    4    | 57   6    57   | 3    9    1    |
 |*36  *36   5    | 9    1    8    | 2    7    4    |
 |----------------+----------------+----------------|
 |*36   2    8    |*136  5    9    | 17   4    67   |
 | 4    5   *13   |*136  7    2    | 18   168  9    |
 | 7   *16   9    |*16   8    4    | 5    3    2    |
 *--------------------------------------------------*


But I suppose you meant the smaller one in r1c69,r2c49,r5c46. However, there's also a UR in r28c78 that solves the puzzle, I'm afraid it won't make the list.

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Re: Unique Loop +1

Postby udosuk » Sat Oct 07, 2006 11:50 am

wapati wrote:URs are fun but common. Unique Loops are unusual, thus more fun!

Very fun puzzle indeed!:)

4 singles -> 1 Unique Loop -> 47 singles solve it!

That's what I call a benchmark puzzle!:)

Too bad the existence of the UR ruined it...:(
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Postby wapati » Sat Oct 07, 2006 2:08 pm

RW wrote:
wapati wrote:Unique Loops are unusual, thus more fun!


Nice puzzle. My first reaction was to use this very uncommon size 10 BUG-lite:

Code: Select all
 *--------------------------------------------------*
 | 8   *13+7*13   | 2    4    57   | 9    16   567  |
 | 9    14   2    | 57   3    6    | 148  18   57   |
 | 5    47   6    | 8    9    1    | 47   2    3    |
 |----------------+----------------+----------------|
 | 1    9    7    | 4    2    3    | 6    5    8    |
 | 2    8    4    | 57   6    57   | 3    9    1    |
 |*36  *36   5    | 9    1    8    | 2    7    4    |
 |----------------+----------------+----------------|
 |*36   2    8    |*136  5    9    | 17   4    67   |
 | 4    5   *13   |*136  7    2    | 18   168  9    |
 | 7   *16   9    |*16   8    4    | 5    3    2    |
 *--------------------------------------------------*


But I suppose you meant the smaller one in r1c69,r2c49,r5c46. However, there's also a UR in r28c78 that solves the puzzle, I'm afraid it won't make the list.

RW


I don't see any elimination from the UR you mentioned.
Please, shed me some light!
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Postby RW » Sat Oct 07, 2006 2:36 pm

wapati wrote:I don't see any elimination from the UR you mentioned.
Please, shed me some light!


Looking at the UR cells:

Code: Select all
    8
148----18


    8
18-----168


Here we have srong links on the 8s for each pair, meaning one of the cells must be an 8 both in row 2 and row 8. So if r2c7=8, then r8c8=8 and obviously the two remaining cells have to be 1, which completes the deadly pattern. Therefore r2c7<>8. Same goes for r8c8<>8. Hope this helped.

If you look carefully, you could also see that even without strong links, if r2c7=1 => r8c8=1 and if r8c8=1 => r2c7=1, and you can eliminate candidate 1 from both those cells also.

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Postby ronk » Sat Oct 07, 2006 3:46 pm

RW wrote:
Code: Select all
 *--------------------------------------------------*
 | 8   *13+7*13   | 2    4    57   | 9    16   567  |
 | 9    14   2    | 57   3    6    | 148  18   57   |
 | 5    47   6    | 8    9    1    | 47   2    3    |
 |----------------+----------------+----------------|
 | 1    9    7    | 4    2    3    | 6    5    8    |
 | 2    8    4    | 57   6    57   | 3    9    1    |
 |*36  *36   5    | 9    1    8    | 2    7    4    |
 |----------------+----------------+----------------|
 |*36   2    8    |*36+1 5    9    | 17   4    67   |
 | 4    5   *13   |*13+6 7    2    | 18   168  9    |
 | 7   *16   9    |*16   8    4    | 5    3    2    |
 *--------------------------------------------------*

Your [edit: 10-cell BUG-Lite+1] doesn't show the usual M+N split for r78c4 ... as I added above. It's rather easy to show that r7c4<>1 and r8c4<>6 because of contradictions in box 7, but since you made no mention of them, I suspect your reasoning was different. What was it?
Last edited by ronk on Sat Oct 07, 2006 2:58 pm, edited 1 time in total.
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Postby ravel » Sat Oct 07, 2006 4:36 pm

I saw it as r1c2=7, otherwise you get that deadly pattern:
Code: Select all
 *--------------------------------------------------*
 | 8   *1/3 *3/1  | 2    4    57   | 9    16   567  |
 | 9    14   2    | 57   3    6    | 148  18   57   |
 | 5    47   6    | 8    9    1    | 47   2    3    |
 |----------------+----------------+----------------|
 | 1    9    7    | 4    2    3    | 6    5    8    |
 | 2    8    4    | 57   6    57   | 3    9    1    |
 |*6/3 *3/6  5    | 9    1    8    | 2    7    4    |
 |----------------+----------------+----------------|
 |*3/6  2    8    |*6/3  5    9    | 17   4    67   |
 | 4    5   *1/3  |*3/1  7    2    | 18   168  9    |
 | 7   *6/1  9    |*1/6  8    4    | 5    3    2    |
 *--------------------------------------------------*
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Postby RW » Sat Oct 07, 2006 4:37 pm

ronk wrote:Your BUG-Lite+10 doesn't show the usual M+N split for r78c4 ... as I added above. It's rather easy to show that r7c4<>1 and r8c4<>6 because of contradictions in box 7, but since you made no mention of them, I suspect your reasoning was different. What was it?


Actually I used kind of a layered BUG-lite reasoning (btw. it should be BUG-lite+1). According to that
Code: Select all
abc abc abc

is just as good as
Code: Select all
ab  ac  bc


In box 8 we have
Code: Select all
136
136
16


that thus can be treated as
Code: Select all
13      36
36  or  13
16      16


I could see that this isn't a real layered BUG-lite, because both alternatives are not possible deadly patterns (as you said 1 can be eliminated from r7c4 and 6 can be eliminated from r8c4). Anyway it can still be used in the same way. As I couldn't decide ifI should describe this as a layered BUG-lite or a BUG-lite+1 after 2 eliminations, I just showed it the way I see it. I don't really make any difference between layered and ordinary BUG-lites, they all work in the same way.

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Postby daj95376 » Sat Oct 07, 2006 5:56 pm

I would like to propose a (slightly) alternate description for the UR. Mainly to have people read it and let me know if I'm wrong. (I'm currently trying to improve my understanding of URs.)

Code: Select all
 *--------------------------------------------------*
 | 8    137  13   | 2    4    57   | 9    16   567  |
 | 9    14   2    | 57   3    6    | 148# 18#  57   |
 | 5    47   6    | 8    9    1    | 47   2    3    |
 |----------------+----------------+----------------|
 | 1    9    7    | 4    2    3    | 6    5    8    |
 | 2    8    4    | 57   6    57   | 3    9    1    |
 | 36   36   5    | 9    1    8    | 2    7    4    |
 |----------------+----------------+----------------|
 | 36   2    8    | 136  5    9    | 17   4    67   |
 | 4    5    13   | 136  7    2    | 18#  168# 9    |
 | 7    16   9    | 16   8    4    | 5    3    2    |
 *--------------------------------------------------*

In the pound (#) cells above, a deadly pattern would exist if both [r2c7]<>4 and [r8c8]<>6 were to occur. In addition, there are four strong links on <8> in [r2c78], [r8c78], [r28c7], and [r28c8]. Now, consider the possible selections to eliminate the deadly pattern -- [r2c7]=4 or [r8c8]=6. No matter which is selected, the strong links on <8> are going to force [r2c8]=8 and [r8c7]=8. To the purists, I believe eliminations are actually performed. I'm just not sure which cells/eliminations.

[Edited:] See comment on UR Type in later post.
Last edited by daj95376 on Sun Oct 08, 2006 5:50 pm, edited 1 time in total.
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Postby ravel » Sat Oct 07, 2006 6:14 pm

What you described is an alternative deduction for eliminating 8 from r2c7 and r8c8 because of the strong links, but it does not solve the puzzle. For this you need:
RW wrote:If you look carefully, you could also see that even without strong links, if r2c7=1 => r8c8=1 and if r8c8=1 => r2c7=1, and you can eliminate candidate 1 from both those cells also.
(this elimination cannot be made without using an "extra cell" not contained in the UR)
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Postby daj95376 » Sat Oct 07, 2006 8:27 pm

ravel, thanks for bringing this to my attention. I still need to convince myself that the elimination of <18> in [r2c7] and [r8c8] are in the same UR. It reminds me of two overlapping and cannibalistic URs.

In my post, I took the more conservative approach of only addressing the forced assignments on <8>. This way needs an X-Wing and XY-Wing to complete the puzzle. If the eliminations on <1> are included in the same UR for <8>, then these wings aren't necessary.

[Edited:]
Last edited by daj95376 on Sat Oct 07, 2006 4:58 pm, edited 1 time in total.
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