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Website · by **denis_berthier** » Sun Sep 18, 2022 5:08 am

.
This is #1359 in mith's list of 63137 min-expand puzzles in T&E(3)
I'll say later why I chose it, but let me already say that is has something new wrt my previous examples.

Code: Select all: +-------+-------+-------+ ! . . . ! . . . ! . . . ! ! 4 . 6 ! . 8 . ! . 2 3 ! ! 7 . . ! . 3 2 ! . . 4 ! +-------+-------+-------+ ! 2 . 8 ! . 6 3 ! 4 . . ! ! 3 4 . ! . 7 . ! 6 . . ! ! . 6 7 ! . . 4 ! . . . ! +-------+-------+-------+ ! . . . ! . . . ! . 9 5 ! ! 8 . 4 ! . . . ! . . 6 ! ! . . . ! . 2 7 ! . 4 1 ! +-------+-------+-------+ .........4.6.8..237...32..42.8.634..34..7.6...67..4..........958.4.....6....27.41;250;48833 SER = 11.7

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 159 123589 12359 ! 145679 1459 1569 ! 1579 15678 789 ! ! 4 159 6 ! 1579 8 159 ! 1579 2 3 ! ! 7 1589 159 ! 1569 3 2 ! 159 1568 4 ! +----------------------+----------------------+----------------------+ ! 2 159 8 ! 159 6 3 ! 4 157 79 ! ! 3 4 159 ! 12589 7 1589 ! 6 158 289 ! ! 159 6 7 ! 12589 159 4 ! 1359 1358 289 ! +----------------------+----------------------+----------------------+ ! 16 1237 123 ! 13468 14 168 ! 2378 9 5 ! ! 8 123579 4 ! 1359 159 159 ! 237 37 6 ! ! 569 359 359 ! 35689 2 7 ! 38 4 1 ! +----------------------+----------------------+----------------------+ 183 candidates.

by **totuan** » Sun Sep 18, 2022 12:23 pm

Code: Select all: *-----------------------------------------------------------------------------* | 159 23 23 |a14579-6 1459b 1569 | 1579 15678 789 | | 4 159 6 | 1579 8 159 | 1579 2 3 | | 7 8 159 | 1569 3 2 | 159 156 4 | |-------------------------+-------------------------+-------------------------| | 2 159 8 | 159 6 3 | 4 157 79 | | 3 4 159 | 12589 7 1589 | 6 158 289 | | 159 6 7 | 12589 159 4 | 1359 1358 289 | |-------------------------+-------------------------+-------------------------| |d16 1237 123 | 13468 c14 168 | 2378 9 5 | | 8 123579 4 | 1359 159 159 | 237 37 6 | |e569 359 359 |f35689 2 7 | 38 4 1 | *-----------------------------------------------------------------------------*

My path for this one:
01: (6)r9c4=r9c1-(6=1)r7c1-(1=4)r7c5-41c5=r1c4 => r1c4<>6

Code: Select all: *-----------------------------------------------------------------------------* |*159 23 23 | 14579 *1459 $1569 |%1579 %15678 %789 | | 4 *159 6 | 1579 8 *159 |%1579 2 3 | | 7 8 *159 |*1569 3 2 | 159 156 4 | |-------------------------+-------------------------+-------------------------| | 2 *159 8 |*159 6 3 | 4 157 79 | | 3 4 *159 | 12589 7 *1589 | 6 158 289 | |*159 6 7 | 12589 *159 4 | 1359 1358 289 | |-------------------------+-------------------------+-------------------------| | 16 1237 123 | 13468 $14 $168 |&2378 9 5 | | 8 123579 4 |#1359 #159 #159 |&237 &7-3 6 | | 569 359 359 | 35689 2 7 | 38 4 1 | *-----------------------------------------------------------------------------*

Tridagon (159) => (4)r1c5=(6)r3c4=(8)r5c6
02: Present as diagram: => r8c8<>3, some singles

Code: Select all: ----------------------(1)r7c6 | || | (8)r5c6----(8)r7c6 | || || (3=159)r8c456---(1=4)r7c5-(4)r1c5 (6)r7c6 || | (6)r3c4-------r1c6=(68-7)r1c89=r12c7-r78c7=r8c8*

Code: Select all: *--------------------------------------------------------------------* | 159 23 23 | 14579 1459 a1569 | 1579 e158-6 89 | | 4 159 6 | 1579 8 159 | 1579 2 3 | | 7 8 159 | 1569 3 2 | 159 156 4 | |----------------------+----------------------+----------------------| | 2 159 8 | 159 6 3 | 4 15 7 | | 3 4 159 | 12589 7 c1589 | 6 d158 289 | | 159 6 7 | 28 159 4 | 159 3 28 | |----------------------+----------------------+----------------------| | 16 7 123 | 13468 14 b168 | 238 9 5 | | 8 12359 4 | 1359 159 159 | 23 7 6 | | 569 359 359 | 35689 2 7 | 38 4 1 | *--------------------------------------------------------------------*

03: (6)r1c6=(6-8)r7c6=r5c6-r5c8=r1c8 => r1c8<>6, some singles

Code: Select all: *--------------------------------------------------------------------* | 159 23 23 | 14579 #1459 6 | 1579 158 89 | | 4 159 6 | 1579 8 159 | 1579 2 3 | | 7 8 159 | 159 3 2 | 159 6 4 | |----------------------+----------------------+----------------------| | 2 159 8 | 159 6 3 | 4 15 7 | | 3 4 159 | 12589 7 #1589 | 6 158 289 | | 159 6 7 | 28 159 4 | 159 3 28 | |----------------------+----------------------+----------------------| | 6-1 7 23-1 | 3468-1*14 *18 | 238 9 5 | | 8 12359 4 | 1359 159 159 | 23 7 6 | | 569 359 359 | 35689 2 7 | 38 4 1 | *--------------------------------------------------------------------*

Tridagon (159) as above => (4)r1c5=(8)r5c6
04: (48)r1c5/r5c6-(48=1)r7c56 => r7c134<>1, some singles
From here, then many way to finish this one

Code: Select all: *--------------------------------------------------------------------* |b159 2 3 | 14579 1459 6 | 1579 c158 89 | | 4 59 6 | 1579 8 159 | 1579 2 3 | | 7 8 159 | 159 3 2 | 159 6 4 | |----------------------+----------------------+----------------------| | 2 59 8 | 159 6 3 | 4 d15 7 | | 3 4 159 | 12589 7 1589 | 6 d158 289 | |a159 6 7 | 28 159 4 | 59-1 3 28 | |----------------------+----------------------+----------------------| | 6 7 2 | 48 14 18 | 3 9 5 | | 8 1 4 | 3 59 59 | 2 7 6 | | 59 3 59 | 6 2 7 | 8 4 1 | *--------------------------------------------------------------------*

05: (1)r6c1=r1c1-r1c8=r45c8 => r6c7<>1

Code: Select all: *--------------------------------------------------------------------* |*159 2 3 |#14579 #1459 6 |#1579 *58 89 | | 4 *59 6 | 1579 8 159 | 1579 2 3 | | 7 8 %159 | 159 3 2 | 159 6 4 | |----------------------+----------------------+----------------------| | 2 *59 8 | 159 6 3 | 4 &15 7 | | 3 4 %159 | 12589 7 1589 | 6 &158 289 | | 159 6 7 | 28 159 4 | 59 3 28 | |----------------------+----------------------+----------------------| | 6 7 2 | 48 14 18 | 3 9 5 | | 8 1 4 | 3 59 59 | 2 7 6 | | 59 3 59 | 6 2 7 | 8 4 1 | *--------------------------------------------------------------------*

06: (1)r4c8=r5c8-r5c3=r3c3-(1=589)r1c189-(5)r1c457=[5’s: r4c2=r2c2-r1c1=r1c8] => r4c8<>5, r4c8=1

Code: Select all: *--------------------------------------------------------------------* | 159 2 3 | 14579 1459 6 | 1579 58 89 | | 4 59 6 | 1579 8 159 | 1579 2 3 | | 7 8 *159 |#159 3 2 |#159 6 4 | |----------------------+----------------------+----------------------| | 2 59 8 |#59 6 3 | 4 1 7 | | 3 4 *159 |%2589-1 7 %589-1 | 6 58 289 | | 159 6 7 | 28 #159 4 |#59 3 28 | |----------------------+----------------------+----------------------| | 6 7 2 | 48 14 18 | 3 9 5 | | 8 1 4 | 3 59 59 | 2 7 6 | | 59 3 59 | 6 2 7 | 8 4 1 | *--------------------------------------------------------------------*

Oddagon (59) => (1)r6c5=r3c47
07: (1)r6c5==r3c47-r3c3=r5c3 => r5c46<>1, stte

Edit: If you eliminate 6’s at r1c8 as second move (based 8’s on column 8) then you can reduce steps to 6 steps, but I like to use tridagon first

Edit 2: Look at: if r6c8<>8 => (6)r1c6=(6-8)r7c6=r5c6-r5c8=r1c8 => r1c8<>6
(78)r1c89=(7)r12c7-r78c7=(7-3)r8c8=(3-8)r6c8=[(6)r1c6=(6-8)r7c6=r5c6-r5c8=r1c8] => r1c8<>6
From here, then no kraken/diagram for this puzzle

Thanks for the puzzle!
totuan

by **eleven** » Sun Sep 18, 2022 4:24 pm

My start was:

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 159 23 23 | 4579 1459 C1569 | 1579 c1578-6 b789 | | 4 159 6 | 1579 8 159 | 1579 2 3 | | 7 8 159 | 1569 3 2 | 159 15+6 4 | +-------------------------+-------------------------+-------------------------+ | 2 159 8 | 159 6 3 | 4 15+7 a79 | | 3 4 159 | 12589 7 A1589 | 6 15+8 289 | | 159 6 7 | 12589 159 4 | 1359 1358 289 | +-------------------------+-------------------------+-------------------------+ | 16 127 123 | 1348 14 B168 | 2378 9 5 | | 8 123579 4 | 1359 159 159 | 237 37 6 | | 569 359 359 | 35689 2 7 | 38 4 1 | +-------------------------+-------------------------+-------------------------+

r345c7 can't all be 15 => 6r3c7|7r4c7|8r5c7:
7r4c7 - r4c9 = (7-8)r1c9 =8r1c8
8r5c7 - r5c6 = (8-6) = 6r1c6
=> -6r1c8

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 159 23 23 |e145679 d1459 a1569 | 1579 1578 789 | | 4 159 6 | 1579 8 159 | 1579 2 3 | | 7 8 159 | 159 3 2 | 159 6 4 | +-------------------------+-------------------------+-------------------------+ | 2 159 8 | 159 6 3 | 4 157 79 | | 3 4 159 | 12589 7 1589 | 6 158 289 | | 159 6 7 | 12589 159 4 | 1359 1358 289 | +-------------------------+-------------------------+-------------------------+ |c16 1237 123 | 13468 c14 b168 | 2378 9 5 | | 8 123579 4 | 1359 159 159 | 237 37 6 | | 569 359 359 | 35689 2 7 | 38 4 1 | +-------------------------+-------------------------+-------------------------+

6r1c6 = r7c6 - (6=14)r7c15 - r1c5 = r1c4 => -6r1c4

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 159 23 23 | 14579 b159+4 6 | 1579 1578 789 | | 4 159 6 | 1579 8 159 | 1579 2 3 | | 7 8 159 | 159 3 2 | 159 6 4 | +-------------------------+-------------------------+-------------------------+ | 2 159 8 | 159 6 3 | 4 157 79 | | 3 4 159 | 12589 7 c159+8 | 6 158 289 | | 159 6 7 | 12589 159 4 | 1359 1358 289 | +-------------------------+-------------------------+-------------------------+ | 16 1237 123 | 13468 a14 d18 | 2378 9 5 | | 8 123579 4 | 1359 159 159 | 237 37 6 | | 569 359 359 | 35689 2 7 | 38 4 1 | +-------------------------+-------------------------+-------------------------+

TH 4r1c5=8r5c6 => (1=4)r7c5 - r1c5 == 8r5c6 - (8=1)r7c6 => -1r7c1234,r8r456

Code: Select all: +----------------------+----------------------+----------------------+ |*159 2 3 | 4579-1 1459 6 |*1579 58-1 89 | | 4 #59 6 | 579-1 8 #59+1 |*1579 2 3 | | 7 8 159 |#59+1 3 2 |*159 6 4 | +----------------------+----------------------+----------------------+ | 2 #59 8 |#59+1 6 3 | 4 15 7 | | 3 4 159 | 12589 7 1589 | 6 158 289 | |*159 6 7 | 28 159 4 |*159 3 28 | +----------------------+----------------------+----------------------+ | 6 7 2 | 48 14 18 | 3 9 5 | | 8 1 4 | 3 59 59 | 2 7 6 | | 59 3 59 | 6 2 7 | 8 4 1 | +----------------------+----------------------+----------------------+

oddagon 59 (#) => -1r12c4,
skyscraper c17 => -1r1c8,
then swordfish 1 c348 => -1r3c7,r5c6 ...
Found no short solution, but just common advanced techniques needed from here

by **shye** » Sun Sep 18, 2022 4:25 pm

hard one
after hidden pair at the start

Code: Select all: .------------------.--------------------.-------------------. | 159 23 23 | 145679 1459 *1569 |#1579 *1578-6 *789 | | 4 159 6 | 1579 8 159 |#1579 2 3 | | 7 8 159 | 1569 3 2 |#159 #156 4 | :------------------+--------------------+-------------------: | 2 159 8 | 159 6 3 | 4 157 79 | | 3 4 159 | 12589 7 *1589 | 6 158 289 | | 159 6 7 |K12589 159 4 | 1359 K1358 K289 | :------------------+--------------------+-------------------: | 16 1237 123 | 13468 14 *168 |*2378 9 5 | | 8 123579 4 | 1359 159 159 |*237 *37 6 | | 569 359 359 | 35689 2 7 | 38 4 1 | '------------------'--------------------'-------------------'

kraken row (8)r6c489
||8r6c4 - 8r5c6 = (8-6)r7c6 = 6r1c6
||(8-3)r6c8 = (3-7)r8c8 = 7b9p14 - (7=1596)b3p1478
||8r6c9 - 8r1c9 = 8r1c8
=> -6r1c8

XSudo Input: Show

Code: Select all: .------------------.---------------------.-----------------. |T159 23 23 | 145679 T1459 1569 | 1579 1578 789 | | 4 T159 6 | 1579 8 T159 | 1579 2 3 | | 7 8 T159 |T#159 3 2 | 159 6 4 | :------------------+---------------------+-----------------: | 2 T159 8 |T#159 6 3 | 4 157 79 | | 3 4 T159 |#12589 7 T1589 | 6 158 289 | |T159 6 7 |#12589 T159 4 | 1359 1358 289 | :------------------+---------------------+-----------------: | 16 1237 123 | 3468-1 #14 168 | 2378 9 5 | | 8 123579 4 | 3-159 #159 #159 | 237 37 6 | | 569 359 359 | 368-59 2 7 | 38 4 1 | '------------------'---------------------'-----------------'

ALS w-wing using trivalue oddagon
T-marked cells cannot all be 159
(1259=8)r3456c4 - 8r5c6 == 4r1c5 - (4=159)b8p256
=> -159r789c4
many singles, a hidden pair, then a small step

empty rectangle
1r1c1 = 1r6c1 - 1b6p7 = 1b6p25
=> -1r1c8

and to finish: (i particularly enjoyed this bit)

Code: Select all: .--------------.-------------------.----------------. | 1-59 2 3 | 14579 1459 6 | 1579 #58 #89 | | 4 #59 6 | 1579 8 159 | 1579 2 3 | | 7 8 S159 |S159 3 2 |*159 6 4 | :--------------+-------------------+----------------: | 2 S59 8 |S159 6 3 | 4 *15 7 | | 3 4 159 | 12589 7 1589 | 6 158 289 | | 159 6 7 | 28 159 4 | 59 3 28 | :--------------+-------------------+----------------: | 6 7 2 | 48 14 18 | 3 9 5 | | 8 1 4 | 3 59 59 | 2 7 6 | | 59 3 59 | 6 2 7 | 8 4 1 | '--------------'-------------------'----------------'

let xy = 59
(x=8y)r1c89 - yr3c7 & yr4c8 = [skyscraper: yr3c3 = yr3c4 - yr4c4 = yr4c2] - (y=x)r2c2
=> -xr1c1 stte

XSudo Input: Show

by **eleven** » Sun Sep 18, 2022 6:51 pm

Ah, nice !

Website · by **denis_berthier** » Mon Sep 19, 2022 5:32 am

.
Thanks for your solution.
My reason for choosing this puzzle is to illustrate an ORk-whip pattern more general than the previously defined ORk-contrad-whips: the ORk part may appear at another place than the final (contradiction) one.
Informally speaking, an ORk-whip (based on some ORk-relation, e.g. an anti-tridagon one) is like a whip, except that some of its CSP-Variables is replaced by an ORk relation, where k-1 candidates are linked to previous right-linking candidates and the remaining one is used as a right linking-candidate for the next step.

Notice the notation for an ORk-whip based on an ORk-relation:
- the full name is ORname-ORk-whip[n], with "n" the total length as usual, "k" the size or the OR relation and "OR name" the short name of this relation.
- I use double curly braces for the ORk part (to recall that it's not a CSP-Variable).

The start is quite easy, using only short reversible chains.

Code: Select all: hidden-pairs-in-a-row: r1{n2 n3}{c2 c3} ==> r1c3≠9, r1c3≠5, r1c3≠1, r1c2≠9, r1c2≠8, r1c2≠5, r1c2≠1 hidden-single-in-a-block ==> r3c2=8 biv-chain[4]: r1n4{c4 c5} - r7c5{n4 n1} - r7c1{n1 n6} - c6n6{r7 r1} ==> r1c4≠6 z-chain[5]: r8n2{c2 c7} - r8n7{c7 c8} - r4n7{c8 c9} - r4n9{c9 c4} - r9n9{c4 .} ==> r8c2≠9 whip[1]: r8n9{c6 .} ==> r9c4≠9 +-------------------+-------------------+-------------------+ ! 159 23 23 ! 14579 1459 1569 ! 1579 15678 789 ! ! 4 159 6 ! 1579 8 159 ! 1579 2 3 ! ! 7 8 159 ! 1569 3 2 ! 159 156 4 ! +-------------------+-------------------+-------------------+ ! 2 159 8 ! 159 6 3 ! 4 157 79 ! ! 3 4 159 ! 12589 7 1589 ! 6 158 289 ! ! 159 6 7 ! 12589 159 4 ! 1359 1358 289 ! +-------------------+-------------------+-------------------+ ! 16 1237 123 ! 13468 14 168 ! 2378 9 5 ! ! 8 12357 4 ! 1359 159 159 ! 237 37 6 ! ! 569 359 359 ! 3568 2 7 ! 38 4 1 ! +-------------------+-------------------+-------------------+ OR3-anti-tridagon[12] for digits 1, 5 and 9 in blocks: b1, with cells: r1c1, r2c2, r3c3 b2, with cells: r1c5, r2c6, r3c4 b4, with cells: r6c1, r4c2, r5c3 b5, with cells: r6c5, r4c4, r5c6 with 3 guardians: n4r1c5 n6r3c4 n8r5c6

This is where the ORk-whips appear:
Trid-OR3-whip[4]: r7c1{n6 n1} - r7c6{n1 n8} - OR3{{n8r5c6 n6r3c4 | n4r1c5}} - r7c5{n4 .} ==> r7c4≠6
z-chain[4]: c7n1{r3 r6} - c1n1{r6 r7} - r7n6{c1 c6} - r1n6{c6 .} ==> r1c8≠1
Trid-OR3-whip[5]: r7c1{n1 n6} - r9n6{c1 c4} - r7c6{n6 n8} - OR3{{n8r5c6 n6r3c4 | n4r1c5}} - r7c5{n4 .} ==> r7c4≠1
Trid-OR3-whip[5]: r7c1{n1 n6} - r9n6{c1 c4} - r7c6{n6 n8} - OR3{{n8r5c6 n6r3c4 | n4r1c5}} - r7c5{n4 .} ==> r7c2≠1
Trid-OR3-whip[5]: r7c1{n1 n6} - r9n6{c1 c4} - r7c6{n6 n8} - OR3{{n8r5c6 n6r3c4 | n4r1c5}} - r7c5{n4 .} ==> r7c3≠1

The end is easy:

Code: Select all: naked-pairs-in-a-column: c3{r1 r7}{n2 n3} ==> r9c3≠3 t-whip[5]: r1n6{c8 c6} - r7n6{c6 c1} - b7n1{r7c1 r8c2} - r8n2{c2 c7} - r8n7{c7 .} ==> r1c8≠7 biv-chain[4]: b3n8{r1c8 r1c9} - c9n7{r1 r4} - c8n7{r4 r8} - c8n3{r8 r6} ==> r6c8≠8 hidden-pairs-in-a-row: r6{n2 n8}{c4 c9} ==> r6c9≠9, r6c4≠9, r6c4≠5, r6c4≠1 biv-chain[3]: r1n6{c6 c8} - c8n8{r1 r5} - c6n8{r5 r7} ==> r7c6≠6 singles ==> r9c4=6, r1c6=6, r3c8=6, r7c1=6, r8c2=1, r8c7=2, r8c8=7, r4c9=7, r7c2=7, r7c3=2, r1c3=3, r1c2=2, r9c2=3,r9c7=8, r7c7=3, r6c8=3, r8c4=3 whip[1]: c8n1{r5 .} ==> r6c7≠1 z-chain[3]: c9n9{r5 r1} - r3n9{c7 c4} - r4n9{c4 .} ==> r5c3≠9 biv-chain[3]: c1n1{r1 r6} - r5c3{n1 n5} - b7n5{r9c3 r9c1} ==> r1c1≠5 biv-chain[3]: r2c2{n5 n9} - b4n9{r4c2 r6c1} - r6c7{n9 n5} ==> r2c7≠5 biv-chain[4]: r5c3{n5 n1} - r6n1{c1 c5} - b8n1{r7c5 r7c6} - c6n8{r7 r5} ==> r5c6≠5 biv-chain[4]: b4n9{r6c1 r4c2} - r2c2{n9 n5} - c6n5{r2 r8} - b8n9{r8c6 r8c5} ==> r6c5≠9 biv-chain[2]: r6n9{c7 c1} - c2n9{r4 r2} ==> r2c7≠9 finned-x-wing-in-rows: n9{r4 r2}{c2 c4} ==> r3c4≠9, r1c4≠9 finned-x-wing-in-rows: n9{r6 r3}{c7 c1} ==> r1c1≠9 stte

by **DEFISE** » Mon Sep 19, 2022 7:38 pm

After basics :

Code: Select all: |--------------------------------------------------------------------| | 159 23 23 | 145679 1459 1569 | 1579 15678 789 | | 4 159 6 | 1579 8 159 | 1579 2 3 | | 7 8 159 | 1569 3 2 | 159 156 4 | |--------------------------------------------------------------------| | 2 159 8 | 159 6 3 | 4 157 79 | | 3 4 159 | 12589 7 1589 | 6 158 289 | | 159 6 7 | 12589 159 4 | 1359 1358 289 | |--------------------------------------------------------------------| | 16 1237 123 | 13468 14 168 | 2378 9 5 | | 8 123579 4 | 1359 159 159 | 237 37 6 | | 569 359 359 | 35689 2 7 | 38 4 1 | |--------------------------------------------------------------------|

Tridagon (1,5,9) in b1p159, b2p267, b4p267, b5p168
With 3 guardians: 4r1c5, 6r3c4, 8r5c6

whip[6]: c8n6{r3 r1}- c6n6{r1 r7}- c6n8{r7 r5}- c8n8{r5 r6}- r6n3{c8 c7}- c7n5{r6 .} => -5r3c8
whip[6]: c8n6{r3 r1}- c6n6{r1 r7}- c6n8{r7 r5}- c8n8{r5 r6}- r6n3{c8 c7}- c7n1{r6 .} => -1r3c8
Single: 6r3c8
whip[4]: r7c1{n6 n1}- r7c5{n1 n4}- r1n4{c5 c4}- r1n6{c4 .} => -6r7c6
Single: 6r1c6

Only 2 two guardians remaining: 4r1c5 and 8r5c6.
Partial-whip[1] from 4r1c5 : r7c5{n4 n1}-
Partial-whip[1] from 8r5c6 : r7c6{n8 n1}-
=> -1r7c1234, -1r8c456

Code: Select all: |-----------------------------------------------------------| | 159 2 3 | 14579 1459 6 | 1579 158 89 | | 4 59 6 | 1579 8 159 | 1579 2 3 | | 7 8 159 | 159 3 2 | 159 6 4 | |-----------------------------------------------------------| | 2 59 8 | 159 6 3 | 4 15 7 | | 3 4 159 | 12589 7 1589 | 6 158 289 | | 159 6 7 | 28 159 4 | 159 3 28 | |-----------------------------------------------------------| | 6 7 2 | 48 14 18 | 3 9 5 | | 8 1 4 | 3 59 59 | 2 7 6 | | 59 3 59 | 6 2 7 | 8 4 1 | |-----------------------------------------------------------|

whip[4]: r1c9{n9 n8}- r6n8{c9 c4}- r7c4{n8 n4}- r1n4{c4 .} => -9r1c5
whip[2]: c2n9{r4 r2}- b2n9{r2c4 .} => -9r4c4
Single(s): 9r4c2, 5r2c2
whip[4]: r5c3{n5 n1}- c1n1{r6 r1}- c8n1{r1 r4}- r4c4{n1 .} => -5r5c6
STTE

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#1359 in T&E(3) min-expands

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