The New Sudoku Players' Forum

by **tarek** » Wed May 06, 2020 3:33 pm

[

Code: Select all: +-------+-------+-------+ | . . 3 | . 7 8 | . . 9 | | . . . | 4 . . | . . 7 | | . 7 . | . . . | 1 . . | +-------+-------+-------+ | 9 . . | . 2 . | . . 8 | | 1 . 5 | . . . | 9 . 2 | | 8 . . | . 5 . | . . 1 | +-------+-------+-------+ | . . 9 | . . . | . 8 . | | 3 . . | . . 6 | . . . | | 2 . . | 9 4 . | 5 . . | +-------+-------+-------+ ..3.78..9...4....7.7....1..9...2...81.5...9.28...5...1..9....8.3....6...2..94.5..

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by **SteveG48** » Wed May 06, 2020 5:56 pm

Code: Select all: *--------------------------------------------------------------* | 56-4 1 3 |bg56 7 8 |ag46 2 9 | | 56 9 2 | 4 cf136 e135 | 8 36 7 | |ag46 7 8 |bg36 9 2 | 1 36-4 5 | *--------------------+--------------------+--------------------| | 9 36 47 | 1367 2 d13 | 346 5 8 | | 1 36 5 | 8 c36 4 | 9 7 2 | | 8 2 47 | 367 5 9 | 346 46 1 | *--------------------+--------------------+--------------------| | 7 4 9 | 135 13 135 | 2 8 6 | | 3 5 1 | 2 8 6 | 7 9 4 | | 2 8 6 | 9 4 7 | 5 1 3 | *--------------------------------------------------------------*

(4=6)r1c7&r3c1 - r13r4 = (63)r25c5 - (3=1)r4c6 - r2c6 = (1-6)r2c5 = (64)r1c47|r3c14 => -4 r1c1,r3c8 ; stte

Or:

Code: Select all: *------------------------------------------------------------* | 456 1 3 |c56 7 8 |bd46 2 9 | | 56 9 2 | 4 c136 c135 | 8 d36 7 | | 46 7 8 | 36 9 2 | 1 346 5 | *-------------------+-------------------+--------------------| | 9 ae36 47 | 1367 2 a1-3 |ae346 5 8 | | 1 36 5 | 8 b36 4 | 9 7 2 | | 8 2 47 | 367 5 9 | 346 46 1 | *-------------------+-------------------+--------------------| | 7 4 9 | 135 13 135 | 2 8 6 | | 3 5 1 | 2 8 6 | 7 9 4 | | 2 8 6 | 9 4 7 | 5 1 3 | *------------------------------------------------------------*

(1=634)r4c267 - (3|4=6)r1c7&r5c5 - (6=513)b2p156 - (3=64)b3p15 - (4=63)r4c27 => -3 r4c6 ; stte

by **Cenoman** » Wed May 06, 2020 10:32 pm

Code: Select all: +------------------+---------------------+-------------------+ | 456 1 3 | 56 7 8 | 46 2 9 | | a56 9 2 | 4 A136 135 | 8 x36 7 | | b46 7 8 | 36 9 2 | 1 c346 5 | +------------------+---------------------+-------------------+ | 9 ze36 47 | 1367 2 1-3 |ze346 5 8 | | 1 36 5 | 8 B36 4 | 9 7 2 | | 8 2 47 | 367 5 9 | 346 yd46 1 | +------------------+---------------------+-------------------+ | 7 4 9 | 135 13 135 | 2 8 6 | | 3 5 1 | 2 8 6 | 7 9 4 | | 2 8 6 | 9 4 7 | 5 1 3 | +------------------+---------------------+-------------------+

Kraken row (6)r2c158
(6)r2c1 - (6=4)r3c1 - r3c8 = r6c8 - (4=63)r4c27
(6)r2c5 - (6=3)r5c5
(6)r2c8 - (6=4)r6c8 - (4=63)r4c27
=> -3 r4c6; ste

by **pjb** » Wed May 06, 2020 10:37 pm

Code: Select all: e456 1 3 |d56 7 8 |c46 2 9 56 9 2 | 4 136 135 | 8 36 7 f46 7 8 |g36 9 2 | 1 346 5 ------------------------+----------------------+--------------------- 9 b36 47 | 367-1 2 a13 |b346 5 8 1 36 5 | 8 36 4 | 9 7 2 8 2 47 | 367 5 9 | 346 46 1 ------------------------+----------------------+--------------------- 7 4 9 |h135 13 35-1 | 2 8 6 3 5 1 | 2 8 6 | 7 9 4 2 8 6 | 9 4 7 | 5 1 3

(1=3)r4c6 - (36=4)r4c27 - (4=6)r1c7 - (5*6=4)r1c14 - (4=6)r3c1 - (6=3)r3c4 - (35*=1)r7c4 => -1 r4c4, r7c6; stte

Phil

Website · by **denis_berthier** » Thu May 07, 2020 6:03 am

After the obvious Singles, three bivalue-chains of length only 3.

Code: Select all: biv-chain[3]: r4c6{n3 n1} - b2n1{r2c6 r2c5} - c5n6{r2 r5} ==> r5c5 ≠ 3 singles ==> r5c5 = 6, r5c2 = 3,> r4c2 = 6 biv-chain[3]: b6n6{r6c8 r6c7} - r6n3{c7 c4} - r3n3{c4 c8} ==> r3c8 ≠ 6 biv-chain[3]: r2c8{n6 n3} - r3c8{n3 n4} - r3c1{n4 n6} ==> r2c1 ≠ 6

by **Ngisa** » Thu May 07, 2020 10:40 am

Code: Select all: +--------------------+------------------------+--------------------+ |a456 1 3 |b5*6 7 8 |b46 2 9 | | 56 9 2 | 4 e13-6 d135 | 8 c36 7 | |h46 7 8 |h36 9 2 | 1 346 5 | +--------------------+------------------------+--------------------+ | 9 36 47 | 1367 2 13 | 346 5 8 | | 1 36 5 | 8 36 4 | 9 7 2 | | 8 2 47 | 367 5 9 | 346 46 1 | +--------------------+------------------------+--------------------+ | 7 4 9 |g135 f13 135 | 2 8 6 | | 3 5 1 | 2 8 6 | 7 9 4 | | 2 8 6 | 9 4 7 | 5 1 3 | +--------------------+------------------------+--------------------+

(4)r1c1 - (4=5*6)r1c47 - (6=3)r2c8 - (35*=1)r2c6 - r2c5 = r7c5 - (5*1=3)r7c4 - (3=64)r3c41 => - 4r1c1; stte

Clement

by **SpAce** » Thu May 07, 2020 11:18 am

Code: Select all: .---------------.--------------------.---------------. | 456 1 3 | d(5)6 7 8 | d46 2 9 | | 56 9 2 | 4 136 135 | 8 36 7 | | d46 7 8 | d(3)6 9 2 | 1 c346 5 | :---------------+--------------------+---------------: | 9 36 b47 | a[71]6-3 2 13 | 346 5 8 | | 1 36 5 | 8 36 4 | 9 7 2 | | 8 2 b47 | 367 5 9 | 346 c46 1 | :---------------+--------------------+---------------: | 7 4 9 | a[1]-35 13 135 | 2 8 6 | | 3 5 1 | 2 8 6 | 7 9 4 | | 2 8 6 | 9 4 7 | 5 1 3 | '---------------'--------------------'---------------'

(17)r74c4 = (7,4)r46c3 - r6=3c8 - (4=635)r1c7,r3c1,r13c4 => -3r4c4, -35 r7c4; stte

uncompressed: Show

7x7 TM: Show

by **SteveG48** » Thu May 07, 2020 7:08 pm

Ngisa wrote:
Code: Select all
+--------------------+------------------------+--------------------+ |a456 1 3 |b5*6 7 8 |b46 2 9 | | 56 9 2 | 4 e13-6 d135 | 8 c36 7 | |h46 7 8 |h36 9 2 | 1 346 5 | +--------------------+------------------------+--------------------+ | 9 36 47 | 1367 2 13 | 346 5 8 | | 1 36 5 | 8 36 4 | 9 7 2 | | 8 2 47 | 367 5 9 | 346 46 1 | +--------------------+------------------------+--------------------+ | 7 4 9 |g135 f13 135 | 2 8 6 | | 3 5 1 | 2 8 6 | 7 9 4 | | 2 8 6 | 9 4 7 | 5 1 3 | +--------------------+------------------------+--------------------+

(4)r1c1 - (4=5*6)r1c47 - (6=3)r2c8 - (35*=1)r2c6 - r2c5 = r7c5 - (5*1=3)r7c4 - (3=64)r3c41 => - 4r1c1; stte

Clement

Clement, I like your clever double use of the five at r1c4, but the final chain seems to say that if r1c1 is not a 4 then r3c1 is. I don't see any elimination.

by **SteveG48** » Thu May 07, 2020 7:22 pm

SpAce wrote:
Code: Select all
.---------------.--------------------.---------------. | 456 1 3 | d(5)6 7 8 | d46 2 9 | | 56 9 2 | 4 136 135 | 8 36 7 | | d46 7 8 | d(3)6 9 2 | 1 c346 5 | :---------------+--------------------+---------------: | 9 36 b47 | a[71]6-3 2 13 | 346 5 8 | | 1 36 5 | 8 36 4 | 9 7 2 | | 8 2 b47 | 367 5 9 | 346 c46 1 | :---------------+--------------------+---------------: | 7 4 9 | a[1]-35 13 135 | 2 8 6 | | 3 5 1 | 2 8 6 | 7 9 4 | | 2 8 6 | 9 4 7 | 5 1 3 | '---------------'--------------------'---------------'

(17)r74c4 = (7,4)r46c3 - r6=3c8 - (4=635)r1c7,r3c1,r13c4 => -3r4c4, -35 r7c4; stte

Now that there is good, clean fun.

by **SpAce** » Fri May 08, 2020 3:37 am

SteveG48 wrote:Now that there is good, clean fun.

Thanks, Steve! Fun yes, clean hmm...

Anyway, you of all people understand why I wrote the last node as I did. I was naturally tempted to write it:

(4=6)r1c7&r3c1 - (6=35)r13c4

...which would have been easier to follow. I just couldn't bring myself to do it, knowing its slight incorrectness. That said, I really have little to no problem at all if others do (like you just did; nice solution btw!). As I've said before, there's very little room for confusion, so I think it's perfectly fine as long as everyone knows how to interpret it (which is quite intuitive). The perfectly correct way to write it (used in my uncompressed variant) is much longer, uglier, and actually harder to read. So, I did what I did to avoid both problems, but the price was a pretty complex node. After that decision I was compelled to compress everything else too so it wouldn't stand out as the only controversial feature in the chain

Btw, I know you guys hate the "3D" compression, but it's mostly there because it's somewhat related to my on-going discussion with Denis (from whom I originally stole the idea; other contributors being SteveK and Allan Barker). Besides, I think this variant without brackets is not nearly as bad as the earlier incarnations, as far as readability goes. Even my own eye never got used to the earlier versions but I think I might be able to live with this one. What do you think? Is it any better or still just as deserving of contempt?

by **eleven** » Fri May 08, 2020 12:12 pm

Code: Select all: *----------------------------------------------------------* | 456 1 3 | 56 7 8 | 46 2 9 | | b56 9 2 | 4 a13-6 a135 | 8 36 7 | | 4-6 7 8 | b36 9 2 | 1 346 5 | |------------------+---------------------+-----------------| | 9 36 47 | 1367 2 #13 | 346 5 8 | | 1 36 5 | 8 #36 4 | 9 7 2 | | 8 2 47 | 367 5 9 | 346 46 1 | |------------------+---------------------+-----------------| | 7 4 9 | 135 13 135 | 2 8 6 | | 3 5 1 | 2 8 6 | 7 9 4 | | 2 8 6 | 9 4 7 | 5 1 3 | *----------------------------------------------------------*

How would you write that ?
(1|6)r4c6,r5c5 => (-16=3|5)r2c56 => 6r3c4|r2c1 => -6r2c5,r3c1; stte

by **Ngisa** » Fri May 08, 2020 1:34 pm

SteveG48 wrote:
Ngisa wrote:
Code: Select all
+--------------------+------------------------+--------------------+ |a456 1 3 |b5*6 7 8 |b46 2 9 | | 56 9 2 | 4 e13-6 d135 | 8 c36 7 | |h46 7 8 |h36 9 2 | 1 346 5 | +--------------------+------------------------+--------------------+ | 9 36 47 | 1367 2 13 | 346 5 8 | | 1 36 5 | 8 36 4 | 9 7 2 | | 8 2 47 | 367 5 9 | 346 46 1 | +--------------------+------------------------+--------------------+ | 7 4 9 |g135 f13 135 | 2 8 6 | | 3 5 1 | 2 8 6 | 7 9 4 | | 2 8 6 | 9 4 7 | 5 1 3 | +--------------------+------------------------+--------------------+

(4)r1c1 - (4=5*6)r1c47 - (6=3)r2c8 - (35*=1)r2c6 - r2c5 = r7c5 - (5*1=3)r7c4 - (3=64)r3c41 => - 4r1c1; stte

Clement

Clement, I like your clever double use of the five at r1c4, but the final chain seems to say that if r1c1 is not a 4 then r3c1 is. I don't see any elimination.

No, I think you have put it the other way around. My assumption is that: (4) is the solution in r1c1, but, the chain shows 4 is in r3c1, so it cannot be in r1c1 as assumed.

by **SpAce** » Fri May 08, 2020 2:33 pm

eleven wrote:How would you write that ?
(1|6)r4c6,r5c5 => (-16=3|5)r2c56 => 6r3c4|r2c1 => -6r2c5,r3c1; stte

Very nice solution! I'm also pretty sure your way of writing it is as good as any. In my experience, trying to write a proper AIC for something like this would probably be very hard and the end result would almost certainly be uglier and harder to understand than yours. (I'll be happy to stand corrected! I don't have enough brain cycles available to even try right now.) Of course it can be turned into a sort of AIC easily:

(DP=1|6)r4c6,r5c5 - (16=3|5)r2c56 - (35=6)r2c1,r3c4 => -6 r2c5,r3c1; stte

That's no different from a contradiction chain, though. Then again, what's wrong with that, if it happens to be the simplest way to express it?

Added. Here's one easy (but redundant) way to write it as a proper AIC:

(6=35)r2c1,r3c4 - (3|5=1)r2c6 - (1=36)b5p35 - (61=3|5)r2c56 - (35=6)r2c1,r3c4 => -6 r2c5,r3c1; stte

Less redundant but more complicated with an almost-Y-Wing:

[(6=5)r2c1 - (5=3)r2c6 - (3=6)r3c4] = (1)r2c6 - r47c6 = (1,36)r2c6,b5p35 - (1|6=3)r2c5 - (3=6)r3c4 => -6 r2c5,r3c1

(Needless to say I prefer the simplest DP-version. Fun to explore some options, though.)

The reason for the complexity can be seen in the matrix. At least I can't write it with anything simpler than a BTM:

6x6 BTM: Show

(Hope Cenoman will correct that matrix if it has problems.)

Edit: And he did!

It doesn't need a BTM, after all (I must have been really blind). Here's the corrected version:

6x6 TM: Show

--
Added. Here's perhaps a slightly more interesting variant, using two almost-Y-Wings:

(6=3)r3c4 - 3r2c5 = Y-Wing(13-36-61)r4c6,r52c5 - 1r2c6 = Y-Wing(65-53-36)r2c16,r3c4 => -6 r2c5,r3c1; stte

...or the same explicitly:

(6=3)r3c4 - 3r2c5 = [(1=3)r4c6-(3=6)r5c5-(6=1)r2c5] - 1r2c6 = [(6=5)r2c1-(5=3)r2c6-(3=6)r3c4] => -6 r2c5,r3c1

--
Edits: added the dual-Y-Wing variant, added the fixed matrix (thanks to Cenoman)

by **SteveG48** » Fri May 08, 2020 5:01 pm

Ngisa wrote:No, I think you have put it the other way around. My assumption is that: (4) is the solution in r1c1, but, the chain shows 4 is in r3c1, so it cannot be in r1c1 as assumed.

Sorry, Clement, you're right. I missed the fact that your chain started with a weak link. Not good on my part, particularly considering that I used to use that form frequently myself.

by **SteveG48** » Fri May 08, 2020 5:48 pm

eleven wrote:
Code: Select all
*----------------------------------------------------------* | 456 1 3 | 56 7 8 | 46 2 9 | | b56 9 2 | 4 a13-6 a135 | 8 36 7 | | 4-6 7 8 | b36 9 2 | 1 346 5 | |------------------+---------------------+-----------------| | 9 36 47 | 1367 2 #13 | 346 5 8 | | 1 36 5 | 8 #36 4 | 9 7 2 | | 8 2 47 | 367 5 9 | 346 46 1 | |------------------+---------------------+-----------------| | 7 4 9 | 135 13 135 | 2 8 6 | | 3 5 1 | 2 8 6 | 7 9 4 | | 2 8 6 | 9 4 7 | 5 1 3 | *----------------------------------------------------------*

How would you write that ?
(1|6)r4c6,r5c5 => (-16=3|5)r2c56 => 6r3c4|r2c1 => -6r2c5,r3c1; stte

You could write it (6=3)r3c4 - (3=5|6)r2c56 - 6r5c5&5r7c6 = (31)b5p35|(31)r47c6 - 1r3c6 = (56)r2c16|(36)b2p67 , but I agree with SpAce. That just ruins the beauty of the solution.

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