## Really tough ...Required Bowman Bingo to solve

Advanced methods and approaches for solving Sudoku puzzles

### Really tough ...Required Bowman Bingo to solve

Below is a puzzle that I could only go so far on and then I was stumped. The puzzle was then entered in a “solver” which was able to solve the puzzle but required about five “Bowman Bingo” steps before doing so. The first puzzle below is one of the “Bowman Bingo” steps that was given. I don’t know understand the logic involved and I wonder if this is a practicle tool to use in trying to solve a puzzle. While this step is involved, it was not the most complicated of the :Bowman Bingo steps given by any means.

Code: Select all
`  *--------------------------------------------------------------------* | 1278   12478  1378   | 3467   268    5      | 389    4678   789    | | 6      24789  389    | 347    238    3478   | 5      478    1      | | 78     5      378    | 1      3468   9      | 3468   2      678    | |----------------------+----------------------+----------------------| | 189    1689   5      | 3469   7      348    | 2      1368   689    | | 3      16789  16789  | 569    568    2      | 1689   1568   4      | | 289    2689   4      | 3569   1      38     | 7      3568   568    | |----------------------+----------------------+----------------------| | 1578   3      178    | 2      45     6      | 148    9      578    | | 4      6789   2      | 57     59     17     | 168    5678   3      | | 1579   1679   1679   | 8      359    1347   | 16     1467   2      | *--------------------------------------------------------------------*`

I colored the following cell Blue .r4c6, r5c5, r6c6, r7c5, r135789c7.....

Then I colored these cell Green r8c4,r8c5,r9c6 and r7c9.

The solution read: r5c7 cannot be (6) because r8c4 and r9c6 are both (7)

I cannot see the logic in that.

Below is this puzzle as it was created.

Code: Select all
`   *-----------------------------------------------------------------------------* | 12789   124789  13789   | 3467    23468   5       | 34689   34678   6789    | | 6       24789   3789    | 347     2348    23478   | 5       3478    1       | | 78      5       378     | 1       3468    9       | 3468    2       678     | |-------------------------+-------------------------+-------------------------| | 189     1689    5       | 3469    7       348     | 2       1368    689     | | 3       126789  16789   | 569     25689   28      | 1689    1568    4       | | 289     2689    4       | 3569    1       238     | 7       3568    5689    | |-------------------------+-------------------------+-------------------------| | 1578    3       178     | 2       45      6       | 148     9       578     | | 4       16789   2       | 579     59      17      | 168     15678   3       | | 1579    1679    1679    | 8       3459    1347    | 146     14567   2567    | *-----------------------------------------------------------------------------*`

I have two questions:

First, Bowman Bingo looks like it would be extermely difficult to find in a puzzle.

Second, is there somebody in this group who is able to solve this puzzle without resorting to Bowman's Bingo? I couldn't solve it but I am still trying do develop my skills at Sudoku. I would assume that this is a difficult puzzle.

Thanks.

Jasper
Jasper32

Posts: 60
Joined: 04 January 2008

I'm not up on Bowman's Bingo, but some of the cells you highlighted are in this chain.

Code: Select all
`[r5c7]=6 [r9c7]=1 [r8c7]=8 [r7c7]=4 [r7c5]=5 ...[r8c5]=9 [r8c4]=7 [r8c6]=1 [r8c2]=6 [r5c3]=6     => [r5c7]<>6`

also

Code: Select all
`[r8c8]=1 [r9c7]=6 \                                       / => [r8c8]<>1                   + [r8c7]=8 [r7c7]=4 [r7c5]=5 [r8c8]=5 +[r8c8]=6 [r9c7]=1 /                                       \ => [r8c8]<>6[r8c8]=8 [r89c7]=16           [r7c7]=4 [r7c5]=5 [r8c8]=5    => [r8c8]<>8`

followed by

Code: Select all
` r8      Naked  Triple                   <> 579  [r8c26] r9  b7  Locked Candidate 1              <> 9    [r9c5]         turbot fish                     <> 7    [r2c8]`

Code: Select all
` +--------------------------------------------------------------------------------+ |  1278    12478   1378    |  3467    2368    5       |  3689    4678    6789    | |  6       24789   3789    |  347     238     23478   |  5       48      1       | |  78      5       378     |  1       3468    9       |  3468    2       678     | |--------------------------+--------------------------+--------------------------| |  189     1689    5       |  3469    7       348     |  2       1368    689     | |  3       126789  16789   |  569     25689   28      |  189     1568    4       | |  289     2689    4       |  3569    1       238     |  7       3568    5689    | |--------------------------+--------------------------+--------------------------| |  1578    3       178     |  2       45      6       |  148     9       578     | |  4       68      2       |  579     59      1       |  68      57      3       | |  1579    1679    1679    |  8       35      347     |  16      14567   2       | +--------------------------------------------------------------------------------+`
Last edited by daj95376 on Mon Mar 24, 2008 1:45 am, edited 3 times in total.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

bowmans bingo

im guessing you where using the online solver from
scanraid.com

is a guess and check method using colored cells.
basically its a trial and error method.

from the listed puzzle befor bingo steps these are the first few moves.

POINTING PAIR: 9s at r1c7/r1c9 points to r1c1, removing 9
POINTING PAIR: 9s at r1c7/r1c9 points to r1c2, removing 9
POINTING PAIR: 9s at r1c7/r1c9 points to r1c3, removing 9
POINTING PAIR: 3s at r4c8/r6c8 points to r1c8, removing 3
POINTING PAIR: 3s at r4c8/r6c8 points to r2c8, removing 3

X-WING (Col->Row) 4 taken off r1c5, based on r37c57
X-WING (Col->Row) 4 taken off r2c5, based on r37c57
X-WING (Col->Row) 4 taken off r9c5, based on r37c57
X-WING (Col->Row) 4 taken off r1c7, based on r37c57
X-WING (Col->Row) 4 taken off r9c7, based on r37c57

ALS/ALS: [r7c5|r8c5] and [r5c7|r7c7|r8c7|r9c7], 4 is restricted common, other common candidate 9 can be removed from r5c5

POINTING TRIPLE: 9s at r4c4/r5c4/r6c4 points to r8c4, removing 9

ALS/ALS: [r3c1|r3c3|r3c9] and [r3c7|r7c7|r8c7|r9c7], 3 is restricted common, other common candidate 6 can be removed from r1c7

ALS/ALS: [r7c5|r8c4|r8c6] and [r7c7|r8c7|r9c7], 4 is restricted common, other common candidate 1 can be removed from r8c8

ALS/ALS: [r7c5|r8c5|r9c5] and [r1c7|r5c7|r7c7|r8c7|r9c7], 4 is restricted common, other common candidate 3 can be removed from r1c5

AIC Rule 2, on 4 (Alternating Inference Chain, length 6):
5[r9c1]=5[r7c1]-5[r7c5]=4[r7c5]-4[r7c7]=4[r9c8]-
- Chain ends r9c1 cannot be 4 and r9c8 cannot be 5 AIC Rule 2, on 5

(Alternating Inference Chain, length 10):
9[r1c9]=9[r1c7]-3[r1c7]=3[r3c7]-4[r3c7]=4[r3c5]-4[r7c5]=5[r7c5]-5[r7c9]=5[r6c9]-
- Chain ends r1c9 cannot be 5 and r6c9 cannot be 9

AIC Rule 5: r1c9 cannot be 6 because either it is 9 or if not 9 then: 9[r1c9]=9[r1c7]-3[r1c7]=3[r3c7]-4[r3c7]=4[r7c7]-4[r9c8]=4[r9c6]-4[r7c5]=4[r3c5]-6[r3c5]=6[r1c4|r1c5]-6[r1c9]=

my own move to solve.

a forcing chain

when R9C6 = 1

than > R8C6(7) > R8C4(5) > R8C5(9) > R7C5(4) > R9C3(3) > R9C7(6) > [R7C7+R8C7+R8C8] (1,8) = error three cells 2 clues left.

which means R9C6 cannot = 1.

R8C6 = 1 :single in box

next forcing chain

when R8C5 = 5
than R8C4 (7) > R7C5(4) > [R8C7+R8C8]{hidden pair} (8+6) > R7C7 + R9C7 (6) = error 2 cells same candidate same box+row.

therefore r8c5 cannot = 5

r8c5 = 9: naked single.

third forcing chain

when R8C2 = 7
than
R8C4 (5) > R7C5(4) > [R8C7+R8C8]{hidden pair}(8+6} > R7C7+R9C7 (1) = error 2 cells same candidate same box/row.

therefor R8C2 cannot = 7

NAKED PAIR (Row): r8c2/r8c7 removes 6/8 from r8c8

SINGLES CHAIN (Type 1): Removing 5 from r6c4

POINTING PAIR: 5s at r5c4/r5c5 points to r5c8, removing 5

SINGLES CHAIN (Type 1): Removing 7 from r2c8

X-CYCLE on 6 (Discontinuous Alternating Nice Loop, length 6):
6[r5c7]-6[r5c3]=6[r9c3]-6[r8c2]=6[r8c7]-6[r5c7]-
- Discontinuity is two weak links joined at r5c7, 6 can be removed from that cell

ALS/ALS: [r8c2] and [r4c1|r4c2|r6c1|r6c2], 6 is restricted common, other common candidate 8 can be removed from r5c2

AIC Rule 2, on 8 (Alternating Inference Chain, length 6):
7[r2c6]=7[r9c6]-4[r9c6]=4[r9c8]-4[r2c8]=8[r2c8]-
- Chain ends r2c6 cannot be 8 and r2c8 cannot be 7

POINTING TRIPLE: 8s at r1c5/r2c5/r3c5 points to r5c5, removing 8

AIC Rule 2, on 1 (Alternating Inference Chain, length 8):
5[r9c1]=5[r9c5]-5[r5c5]=6[r5c5]-6[r5c3]=6[r9c3]-6[r9c7]=1[r9c7]-
- Chain ends r9c1 cannot be 1

AIC Rule 2, on 7 (Alternating Inference Chain, length 8):
6[r9c3]=6[r5c3]-6[r5c5]=5[r5c5]-5[r5c4]=5[r8c4]-7[r8c4]=7[r9c6]-
- Chain ends r9c3 cannot be 7 and r9c6 cannot be 6

AIC Rule 2, on 4 (Alternating Inference Chain, length 8):
6[r9c3]=6[r5c3]-6[r5c5]=5[r5c5]-5[r7c5]=4[r7c5]-4[r7c7]=4[r9c8]-
- Chain ends r9c3 cannot be 4 and r9c8 cannot be 6

POINTING PAIR: 6s at r8c7/r9c7 points to r3c7, removing 6

APE: Row Pair r3c7 / r3c9 reduced from 3/4/8->3/4/8 and 6/7/8->6/7
- PAIR combination 7/8 found in r3c1
- PAIR combination 4/8 found in r2c8
- TRIPLE combinations 7/8 r3c1 + 3/7/8 r3c3

AIC Rule 2, on 9 (Alternating Inference Chain, length 10):
5[r5c4]=5[r5c5]-5[r7c5]=4[r7c5]-4[r7c7]=4[r3c7]-3[r3c7]=3[r1c7]-9[r1c7]=9[r5c7]-
- Chain ends r5c4 cannot be 9

NAKED PAIR (Box): r5c4/r5c5 removes 6 from r4c4
NAKED PAIR (Box): r5c4/r5c5 removes 6 from r6c4
NAKED PAIR (Row): r5c4/r5c5 removes 6 from r5c2
NAKED PAIR (Row): r5c4/r5c5 removes 6 from r5c3
NAKED PAIR (Row): r5c4/r5c5 removes 6 from r5c8

SINGLE: r9c3 set to 6, unique in Column -inducing a cascade of singles.

XY CHAIN length=4, 9 taken off r5c2, chain ends: r5c7 and r9c2
XY CHAIN length=4, 7 taken off r9c2, chain ends: r5c2 and r9c8
SINGLE: r2c3 set to 9, unique in Row
+more singles

LBR: 3 exists only in box 2 and row B, can remove from r1c4
LBR: 3 exists only in box 2 and row B, can remove from r3c5

Y-WING 8 taken off r4c1 - using r3c1 r3c9 r4c9
Y-WING 1 taken off r4c8 - using r4c2 r4c9 r5c8
Y-WING 1 taken off r5c2 - using r4c2 r4c9 r5c8
Y-WING 1 taken off r5c3 - using r4c2 r4c9 r5c8

some singles.

XY CHAIN length=5, 8 taken off r3c7, chain ends: r2c8 and r3c1
XY CHAIN length=5, 8 taken off r4c8, chain ends: r2c8 and r4c9
XY CHAIN length=5, 8 taken off r6c8, chain ends: r2c8 and r4c9

SINGLE: r2c8 set to 8, unique in Column
SINGLE: r9c8 set to 4, unique in Column

SINGLES CHAIN (Type 2): Removing 7 from r1c8
SINGLES CHAIN (Type 2): Removing 7 from r2c6
SINGLES CHAIN (Type 2): Removing 7 from r3c1
SINGLES CHAIN (Type 2): Removing 7 from r7c9
SINGLES CHAIN (Type 2): Removing 7 from r8c4
SINGLES CHAIN (Type 2): Removing 7 from r9c1

cascade of singles at this point.
puzzle solves

217485369649723581853169427165974238378652914924318756731246895482591673596837142
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1085
Joined: 05 September 2006

### Re: Really tough ...Required Bowman Bingo to solve

Jasper32 wrote:Below is a puzzle that I could only go so far on and then I was stumped.
is there somebody in this group who is able to solve this puzzle without resorting to Bowman's Bingo? I couldn't solve it but I am still trying do develop my skills at Sudoku. I would assume that this is a difficult puzzle.

First, the puzzle without the PMs and without the 2 extra values (r9c9=2 and r5c6=2) is:
Code: Select all
`.....5...6.....5.1.5.1.9.2...5.7.2..3.......4..4.1.7...3.2.6.9.4.2.....3...8.....`

Here is another solution with no Bowman Bingo (= T&E), no ALS, no use of subsets in chains.
The longest chain used has length 5 (5 cells, 10 candidates).
nrc(z)t chains are defined here: http://forum.enjoysudoku.com/viewtopic.php?t=5591

***** SudoRules version 13 *****
hidden-single-in-a-row ==> r9c9 = 2
row r2 interaction-with-block b1 ==> r1c3 <> 9, r1c2 <> 9, r1c1 <> 9
column c7 interaction-with-block b3 ==> r2c8 <> 3, r1c8 <> 3
x-wing-in-rows n4{r3 r7}{c5 c7} ==> r9c7 <> 4, r9c5 <> 4, r2c5 <> 4, r1c7 <> 4, r1c5 <> 4
nrc3-chain n4{r9c8 r9c6} - {n4 n5}r7c5 - n5{r7c1 r9c1} ==> r9c8 <> 5
nrct3-chain n1{r8c6 r9c6} - {n1 n6}r9c7 - n6{r9c3 r8c2} ==> r8c2 <> 1
nrct3-chain n3{r1c7 r3c7} - n4{r3c7 r3c5} - n6{r3c5 r3c9} ==> r1c7 <> 6
nrc4-chain n3{r1c7 r3c7} - n4{r3c7 r7c7} - n4{r7c5 r9c6} - n3{r9c6 r9c5} ==> r1c5 <> 3
nrct4-chain n5{r8c8 r7c9} - {n5 n4}r7c5 - n4{r9c6 r9c8} - n7{r9c8 r8c8} ==> r8c8 <> 8
nrct3-chain {n1 n6}r9c7 - n6{r9c3 r8c2} - n8{r8c2 r8c7} ==> r8c7 <> 1
nrct4-chain n1{r8c6 r8c8} - n5{r8c8 r7c9} - n7{r7c9 r9c8} - n4{r9c8 r9c6} ==> r9c6 <> 1
hidden-single-in-a-block ==> r8c6 = 1
nrct4-chain n5{r8c8 r7c9} - {n5 n4}r7c5 - n4{r9c6 r9c8} - n7{r9c8 r8c8} ==> r8c8 <> 6
hidden-pairs-in-a-row {n6 n8}r8{c2 c7} ==> r8c2 <> 9
row r8 interaction-with-block b8 ==> r9c5 <> 9
hidden-pairs-in-a-row {n6 n8}r8{c2 c7} ==> r8c2 <> 7
nrc2-chain n6{r8c7 r8c2} - n6{r9c3 r5c3} ==> r5c7 <> 6
nrc2-chain n7{r8c8 r8c4} - n7{r9c6 r2c6} ==> r2c8 <> 7
nrc3-chain {n8 n4}r2c8 - n4{r9c8 r9c6} - n7{r9c6 r2c6} ==> r2c6 <> 8
column c6 interaction-with-block b5 ==> r5c5 <> 8
nrc3-chain {n8 n6}r8c2 - n6{r9c3 r5c3} - n7{r5c3 r5c2} ==> r5c2 <> 8
nrct4-chain n9{r1c9 r1c7} - n3{r1c7 r3c7} - n4{r3c7 r3c5} - n6{r3c5 r3c9} ==> r1c9 <> 6
nrc5-chain n9{r8c5 r5c5} - n9{r5c7 r1c7} - n3{r1c7 r3c7} - n4{r3c7 r3c5} - {n4 n5}r7c5 ==> r8c5 <> 5
naked-single ==> r8c5 = 9
nrc2-chain n5{r6c9 r7c9} - n5{r8c8 r8c4} ==> r6c4 <> 5
row r6 interaction-with-block b6 ==> r5c8 <> 5
nrczt4-chain n2{r1c5 r2c6} - n7{r2c6 r9c6} - {n7 n5}r8c4 - n5{r9c5 r5c5} ==> r5c5 <> 2
column c5 interaction-with-block b2 ==> r2c6 <> 2
nrc4-chain n7{r9c6 r8c4} - n5{r8c4 r5c4} - {n5 n6}r5c5 - n6{r5c3 r9c3} ==> r9c3 <> 7
nrc4-chain n4{r9c8 r9c6} - {n4 n5}r7c5 - {n5 n6}r5c5 - n6{r5c3 r9c3} ==> r9c8 <> 6
block b9 interaction-with-column c7 ==> r3c7 <> 6
nrc3-chain n6{r3c9 r3c5} - n4{r3c5 r3c7} - {n4 n8}r2c8 ==> r3c9 <> 8
nrc4-chain {n1 n6}r9c7 - n6{r9c3 r5c3} - {n6 n5}r5c5 - n5{r9c5 r9c1} ==> r9c1 <> 1
nrczt4-chain {n8 n4}r2c8 - n4{r3c7 r3c5} - n8{r3c5 r3c7} - n8{r8c7 r8c2} ==> r2c2 <> 8
nrczt4-chain n3{r1c7 r3c7} - n4{r3c7 r3c5} - {n4 n7}r2c6 - {n7 n3}r2c4 ==> r1c4 <> 3
nrc5-chain {n1 n6}r9c7 - n6{r9c3 r5c3} - {n6 n5}r5c5 - {n5 n4}r7c5 - n4{r9c6 r9c8} ==> r9c8 <> 1
column c8 interaction-with-block b6 ==> r5c7 <> 1
nrct3-chain n9{r1c9 r1c7} - {n9 n8}r5c7 - n8{r8c7 r7c9} ==> r1c9 <> 8
nrct3-chain {n9 n8}r5c7 - n8{r6c9 r7c9} - n5{r7c9 r6c9} ==> r6c9 <> 9
nrct4-chain {n9 n8}r5c7 - n8{r8c7 r7c9} - n5{r7c9 r8c8} - n5{r8c4 r5c4} ==> r5c4 <> 9
naked-pairs-in-a-block {n5 n6}{r5c4 r5c5} ==> r6c4 <> 6, r4c4 <> 6
block b5 interaction-with-row r5 ==> r5c8 <> 6, r5c3 <> 6
naked and hidden singles ==> r9c3 = 6, r8c2 = 8, r8c7 = 6, r9c7 = 1
block b5 interaction-with-row r5 ==> r5c2 <> 6
nrc3-chain n7{r2c6 r9c6} - {n7 n9}r9c2 - n9{r2c2 r2c3} ==> r2c3 <> 7
nrc3-chain n7{r5c3 r5c2} - {n7 n9}r9c2 - n9{r2c2 r2c3} ==> r5c3 <> 9
hidden-single-in-a-column ==> r2c3 = 9
row r2 interaction-with-block b2 ==> r3c5 <> 3
nrct3-chain {n7 n8}r3c1 - n8{r6c1 r5c3} - n7{r5c3 r5c2} ==> r2c2 <> 7
row r2 interaction-with-block b2 ==> r1c4 <> 7
nrct3-chain {n7 n8}r3c1 - n8{r6c1 r5c3} - n7{r5c3 r5c2} ==> r1c2 <> 7
xy4-chain {n9 n8}r5c7 - {n8 n4}r7c7 - {n4 n7}r9c8 - {n7 n9}r9c2 ==> r5c2 <> 9
hidden singles ==> r5c7 = 9, r1c9 = 9
hidden-pairs-in-a-block {n6 n7}{r1c8 r3c9} ==> r1c8 <> 8, r1c8 <> 4
xy3-chain {n8 n6}r4c9 - {n6 n7}r3c9 - {n7 n8}r3c1 ==> r4c1 <> 8
nrc3-chain {n1 n9}r4c1 - n9{r9c1 r9c2} - n7{r9c2 r5c2} ==> r5c2 <> 1
nrc3-chain {n8 n7}r3c1 - n7{r3c9 r7c9} - n8{r7c9 r7c7} ==> r3c7 <> 8
xyzt4-chain {n1 n9}r4c1 - {n9 n6}r4c2 - {n6 n8}r4c9 - {n8 n1}r5c8 ==> r5c3 <> 1
hidden-single-in-a-row ==> r5c8 = 1
nrc4-chain n4{r2c2 r1c2} - {n4 n6}r1c4 - {n6 n7}r1c8 - {n7 n4}r9c8 ==> r2c8 <> 4
naked and hidden singles ==> r2c8 = 8, r1c7 = 3, r3c7 = 4, r7c7 = 8, r9c8 = 4, r7c5 = 4, r3c3 = 3
nrczt2-chain n7{r3c1 r3c9} - n7{r7c9 r7c3} ==> r9c1 <> 7
nrc3-chain n7{r2c4 r8c4} - n5{r8c4 r9c5} - n3{r9c5 r2c5} ==> r2c4 <> 3
column c4 interaction-with-block b5 ==> r6c6 <> 3, r4c6 <> 3
naked-pairs-in-a-block {n2 n8}{r5c6 r6c6} ==> r4c6 <> 8
naked and hidden singles ==> r4c6 = 4, r4c9 = 8
nrc4-chain {n6 n7}r1c8 - n7{r8c8 r8c4} - n5{r8c4 r9c5} - {n5 n6}r5c5 ==> r1c5 <> 6
nrc3-chain n8{r3c1 r3c5} - {n8 n2}r1c5 - n2{r1c1 r6c1} ==> r6c1 <> 8
... (naked and hidden singles)...

217485369
649723581
853169427
165974238
378652914
924318756
731246895
482591673
596837142

Notice that in this solution r5c6=2 is obtained only in the final NS and HS steps.
denis_berthier
2010 Supporter

Posts: 1377
Joined: 19 June 2007
Location: Paris

Hi Jasper

I checked this puzzle starting as Denis.

1= 000005000
2= 600000501
3= 050109020
4= 005070200
5= 300000004
6= 004010700
7= 030206090
8= 402000003
9= 000800000

I am surprised a solver used "Bowman Bingo" to solve it.

No need of ALS, "T" chains...

You can solve it exclusively using basic AIC's (about 30 are needed)
champagne
2017 Supporter

Posts: 7033
Joined: 02 August 2007
Location: France Brittany

champagne wrote:You can solve it exclusively using basic AIC's (about 30 are needed)

Unless you put some subsets in your "basic" AICs, I'd really like to see that solution.
denis_berthier
2010 Supporter

Posts: 1377
Joined: 19 June 2007
Location: Paris

Denis wrote
Unless you put some subsets in your "basic" AICs, I'd really like to see that solution

I don't know what are "subsets", but here is the answer.
You will find groups for sure, especially in "OR" cleanings, but nothing more.
All this is level one in my process.

1= 000005000
2= 600000501
3= 050109020
4= 005070200
5= 300000004
6= 004010700
7= 030206090
8= 402000003
9= 000800000

1 r9c9=2 B
-> column 7 digit 3 in box 3
-> row 2 digit 9 in box 1
XWing digit 4 columns 57 rows 37

Code: Select all
`1278 12478  1378  |3467 2368  5     |3l689a 4678   6789A 6    24789  3789  |347  238   23478 |5      478    1     78   5      378   |1    34c68 9     |3L4C68 2      678   --------------------------------------------------------189  1689   5     |3469 7     348   |2      1368   689   3    126789 16789 |569  25689 28    |1689A  1568   4     289  2689   4     |3569 1     238   |7      3568   5689  --------------------------------------------------------1578 3      178   |2    4C5c  6     |14c8   9      578   4    16789  2     |579  59    17    |168    15678  3     1579 1679   1679  |8    359   134c7 |16     14C567 2 `

[]9r8c4.î - 9r8c5 = 5r8c5 - 5r7c5.c = 4r3c7.C - 3r3c7 = 3r1c7 - 9r1c7.a = 9r5c7.A - 9r5c5.î
#9r8c4 #9r5c5

Code: Select all
`1278 12478  1378  |3467 2368    5        |3689 4678  6789 6    24789  3789  |347  238     2U347z8ë |5    478   1    78   5      378   |1    3468    9        |3468 2     678  ---------------------------------------------------------189  1689   5     |3469 7       348      |2    1368  689  3    126789 16789 |569  2U5Z68ë 28       |1689 1568  4    289  2689   4     |3569 1       238      |7    3568  5689 ---------------------------------------------------------1578 3      178   |2    45      6        |148  9     578  4    16789  2     |5Z7z 59      17       |168  15678 3    1579 1679   1679  |8    359     1347     |16   14567 2 `

[]2r5c5.U - 5r5c5.Z = 7r2c6.z - 2r2c6.U
[]8r5c5.ë - 5r5c5.Z = 7r2c6.z - 8r2c6.ë
#2r5c5 #2r2c6 #8r5c5 #8r2c6

Code: Select all
`1278 12478  1378   |346y7 2368  5     |3o689a 4678   6789A 6    24789  3789   |347   238   347y  |5      478    1     78   5      378    |1     34d68 9     |3O4D68 2      678   ----------------------------------------------------------189  1689   5      |3469  7     348   |2      1368   689   3    126789 16m789 |569   5Y6y  28    |1t689A 1568   4     289  2689   4      |3569  1     238   |7      3568   5689  ----------------------------------------------------------1578 3      178    |2     4D5d  6     |14d8   9      578   4    16789  2      |5Y7y  59    17    |168    15678  3     1579 1679   16M79  |8     359   134d7 |1Ë6ë   14D567 2`

[]1r5c7.t - 1r9c7 = 6r9c7 - 6r9c3.M = 6r5c3.m - 6r5c5.y = 5r8c4.Y - 5r7c5.d = 4r3c7.D - 3r3c7 = 3r1c7 - 9r1c7.a = 9r5c7.A - 1r5c7.t
#1r5c7 #1r89c8

Code: Select all
`1278  12478  1378  |3467 2368 5      |3689  4678  6789 6     24789  3789  |347  238  347    |5     478   1     78    5      378   |1    3468 9      |34D68 2     678  -------------------------------------------------------189   1689   5     |3469 7    348    |2     1368  689   3     126789 16789 |569  56   28     |689   1568  4     289   2689   4     |3569 1    238    |7     3568  5689 ------------------------------------------------------15k78 3      178   |2    45   6      |14d8  9     578 4     16789  2     |57   59   17     |168   5678  3     15K79 1679   1679  |8    359  134d7  |16    4D567 2`

5r7c5.d - 5r7c1.k =>4r9c8;5r9c1 clear 5r9c8

Code: Select all
`1278   12478  1378   |346w7 2368  5       |3o689a 4678  6789A 6      24789  3789   |347   238   347w    |5      478   1     78     5      378    |1     34d68 9       |3O4D68 2     678   -------------------------------------------------------------189    1689   5      |3469  7     348     |2      1368  689   3      126789 16m789 |569   5W6w  28      |689A   1568  4     289    2689   4      |3569  1     238     |7      3568  5r689 -------------------------------------------------------------15J78  3      178    |2     4D5d  6       |1S4d8  9     5R7â8 4      16y789 2      |5W7w  59    1n7N    |168    5r678 3     15j79ç 1679   16M79  |8     3i5J9 1N3I4d7 |1É6é   4D67  2   `

[]9r1c7.a - 3r1c7 = 3r3c7 - 4r3c7.D = 5r7c5.d - 5r7c9.R
9r1c9.A;5r6c9.r clear 9r6c1

[]9r1c7.a - 3r1c7 = 3r3c7 - 4r3c7.D = 5r7c5.d - 5r8c4.W
9r1c9.A;6r1c4.w clear 6r1c9 9r5c7.A;6r5c5.w clear 6r5c7

[]9r1c7.a - 3r1c7 = 3r3c7 - 4r3c7.D = 5r7c5.d - 5r9c5.J = 5r9c1 - 9r9c1.ç
9r5c7.A;9r46c1.Ç clear 9r5c23

[]5r7c5.d - 5r8c4.W = 6r5c5.w - 6r5c3.m
4r9c8.D;6r9c3.M clear 6r9c8

[]3r9c6.I - 4r9c6.d = 4r3c7.D - 3r3c7.O
3r9c5.i;3r1c7.o clear 3r1c5

[]5r9c5.J - 5r8c4.W = 6r5c5.w - 6r5c3.m = 6r9c3.M - 6r9c7 = 1r9c7 - 1r7c7.S
5r9c1.j;1r7c13.s clear 1r9c1

[]6r5c3.m - 6r5c5.w = 5r8c4.W - 5r8c8.r = 5r7c9.R - 7r7c9.â
6r9c3.M;7r7c13.Â clear 7r9c3

[]1r9c6.N - 1r9c7 = 6r9c7 - 6r8c78.Y
1r8c6.n;6r8c2.y clear 1r8c2

[]3r3c7.O - 4r3c7.D = 5r7c5.d - 5r8c4.W
3r1c7.o;6r1c4.w clear 6r1c7;3r1c4

[]5r8c4.W - 5r8c8.r = 5r7c9.R - 7r7c9.â
7r8c4.w;7r7c13.Â clear 7r8c2
7r2c6.w;7r89c8.Â clear 7 r2c8

Code: Select all
`1278 12478 1378 |467  268   5     |389    4678   789  6    24789 3789 |347  238   347   |5      48     1    78   5     378  |1    34e68 9     |34E6z8 2      678  -----------------------------------------------------189  1689  5    |3469 7     348   |2      1368   689  3    12678 1678 |569  56    28    |89     1568   4    289  2689  4    |3569 1     238   |7      3568   5r68 -----------------------------------------------------1578 3     178  |2    4E5e  6     |14e8   9      5R78 4    689   2    |57   59    17    |168    5r6z78 3    579  1679  169  |8    359   134e7 |16     4E7e   2  `

[]6r8c8.z - 5r8c8.r = 5r7c9.R - 5r7c5.e = 4r3c7.E - 6r3c7.z
#6r3c7 #6r8c8

Code: Select all
`1278 12478  1378  |46y7 268    5     |389  46f78 789  6    24789d 3789D |347  238    347y  |5    4Ç8ç  1    78   5      378   |1    34e6f8 9     |34E8 2     6F78 -----------------------------------------------------189  1689   5     |3469 7      348   |2    1368  689  3    12678  16q78 |569  5Y6y   28    |89   1568  4    289  2689   4     |3569 1      238   |7    3568  5t68 -----------------------------------------------------1578 3      178   |2    4E5e   6     |14e8 9     5T78 4    689    2     |5Y7y 59     17    |168  5t78  3    579  1679   16Q9d |8    359    134e7 |16   4E7e  2`

[]9r9c3.d - 6r9c3.Q = 6r5c3.q - 6r5c5.y = 5r8c4.Y - 5r7c5.e = 4r3c7.E - 4r2c8.Ç
9r2c3.D;8r2c8.ç clear 8r2c3

[]6r3c5.f - 4r3c5.e = 4r3c7.E - 4r2c8.Ç
6r3c9.F;8r2c8.ç clear 9r3c9

[]5r7c9.T - 5r7c5.e = 4r3c7.E - 4r2c8
5r8c8.t;8r2c8.ç clear 8r8c8
->LS2 cells 48 digits 57 row 8
->LS2 digits 68 cells 27 row 8
2 r8c5=9 R
3 r8c6=1 R

Code: Select all
`1278  12478  1378  |46J7  268   5     |389 4678  789  6     24789d 3r79D |347   238   347J  |5   48    1    78    5      378   |1     3r468 9     |348 2     67   -----------------------------------------------------189   1689   5     |3469  7     348   |2   1368  689  3     12678  16o78 |569   5j6J  28    |89  15T68 4    289   2689   4     |35T69 1     238   |7   3568  5J68 -----------------------------------------------------15L78 3      178   |2     45    6     |148 9     5j78 4     68     2     |5j7J  9     1     |68  5J7j  3    5l79  1679   16O9d |8     3l5L  3L47j |16  47    2`

[]3r3c5.r - 3r9c5.l = 5r9c5.L - 5r8c4.j = 6r5c5.J - 6r5c3.o = 6r9c3.O - 9r9c3.d = 9r2c3 - 3r2c3.r
[]5r5c8.T - 5r8c8.J = 5r8c4.j - 5r6c4.T
#3r2c3 #3r3c5 #5r5c8 #5r6c4

Code: Select all
`1278 12478 1378 |46i7  268  5    |389b 4678  789B  6    24789 79   |347   238  347i |5    48    1     78   5     378  |1     468  9    |348  2     67    --------------------------------------------------189  1689  5    |3469  7    348  |2    1368  689b  3    12678 1678 |5i69b 5I6i 28   |8b9B 168   4     289  2689  4    |369   1    238  |7    35I68 5i68  --------------------------------------------------1578 3     178  |2     45   6    |148  9     5I78W 4    68    2    |5I7i  9    1    |68   5i7I  3     579  1679  169  |8     35   347I |16   47    2   `

[]8r5c7.b - 8r78c7 = 8r7c9 - 5r7c9.I = 5r5c4.i - 9r5c4.b
all 'b' cleared
4 r1c9=9 B
5 r5c7=9 B

->LS2 cells 45 digits 56 row 5
->LS2 cells 45 digits 56 box 5
->LS2 digits 67 cells 29 box 3
6 r9c3=6 C

7 r2c3=9 C
8 r8c2=8
9 r8c7=6 B
10 r9c7=1

->XY WING pivot= r3c9 67 (1)=r3c1 78 (2)=r4c9 68
->UR 3 twins P1=r1c7 38 P2=r1c3 1378 P3=r3c7 348 P4=r3c3 37

Code: Select all
`12m78 1s24b7 13a78o |4B6h7u 2c68   5      |3A8a  6e7E   9      6     2c4B7u 9      |3t47   2C3K8d 347h   |5     4d8D   1      7x8X  5      3A7a   |1      4d6e8  9      |3a4D8 2      6E7e   --------------------------------------------------------------1y9Y  16n9   5      |34f9p  7      34F8w  |2     1q3r68 6z8Z   3     12g7i  17I8O  |5h6H   5H6h   2G8g   |9     1Q8q   4      2M8o9 26N9   4      |3p9P   1      2g38   |7     3R5H68 5h68   --------------------------------------------------------------1j5K7 3      1J7j   |2      4D5d   6      |4d8D  9      5H7E8d 4     8      2      |5H7h   9      1      |6     5h7H   3      5k79l 7l9L   6      |8      3k5K   3K4d7H |1     4D7d   2`

A nice loop with clearings
[]6r3c5.e - 6r5c5.h = 7r8c8.H - 7r7c9.E
three clearing loops
[]8r7c9.d - 7r7c9.E = 6r3c5.e - 4r3c5.d
[]9r9c1.l - 9r4c1 = 1r4c1 - 1r45c2 = 1r1c2 - 4r1c2 = 4r1c4.B - 6r1c4.E = 7r7c13.e - 7r9c2.l
[]7r2c2.u - 7r3c1.x = 8r3c1 - 8r1c3.o = 8r5c3.O - 7r5c3 = 7r5c2 - 7r2c2.u

all 'd' 'l' 'u' cleared

the game is nearly over
champagne
2017 Supporter

Posts: 7033
Joined: 02 August 2007
Location: France Brittany

champagne wrote:I don't know what are "subsets", but here is the answer.
You will find groups for sure, especially in "OR" cleanings, but nothing more.

Although the details of your listing are Chinese for me (not only because of the tags everywhere), this solution obviously doesn't satisfy your claim:
- an AIC with "ORs" is certainly not what anyone would call a "basic" AIC.
- I can also see an UR. Unless UR means anything else than the usual "unique rectangle", you're using uniqueness.
- I don't know what an "or cleaning" is, but if it is a conclusion of type "not C1 or not C2" (where Ci are candidates), this amounts to T&E.
denis_berthier
2010 Supporter

Posts: 1377
Joined: 19 June 2007
Location: Paris

denis wrote
Although the details of your listing are Chinese for me (not only because of the tags everywhere), this solution obviously doesn't satisfy your claim:
- an AIC with "ORs" is certainly not what anyone would call a "basic" AIC.
- I can also see an UR. Unless UR means anything else than the usual "unique rectangle", you're using uniqueness.
- I don't know what an "or cleaning" is, but if it is a conclusion of type "not C1 or not C2" (where Ci are candidates), this amounts to T&E.

You should for sure spend the few minutes necesseraly to understand how works the full tagging. I did it with your method to have a good idea of what is behind "t" chains.

"OR" cleaning is nothing else that what you are doing with your chains.

a canonical AIC in full tagging has a weak link on each end. You are working exclusively with AIC's having a strong link at each end (a OR condition), this is what is done in full tagging level 1 with the switch from an weak link [AB] to the "OR" ab. (later on, only closed loop are used) .

UR is for sure Unique Rectangle. I see no reaon why ths should be excluded as a logic rule. By the way, it comes so late that it is meaningless to qualify the puzzle.

denis wrote

- I don't know what an "or cleaning" is, but if it is a conclusion of type "not C1 or not C2" (where Ci are candidates), this amounts to T&E.

I don't know why you are always suspecting others to use T&E. If XYWing is T&E, if cleaning using an open AIC is T&E then, what I am doing is T&E, and you as well.

denis wrote
Although the details of your listing are Chinese for me

I would give a personnal answer. I like density of "T" chains, but believe me, it's not so easy to check.

When you have a serie of 30 to 40 such chains withour any intermediate situation, it is a kind of punishment.

I chose to give intermediate positions not only because I am tagging, but also to facilitate decoding of the solution
champagne
2017 Supporter

Posts: 7033
Joined: 02 August 2007
Location: France Brittany

champagne wrote:"OR" cleaning is nothing else that what you are doing with your chains.

Very interesting. Are you then using disguised forms of nrczt-chains? (In this case, how can you claim that they weren't needed for this puzzle?)
In any case, I'm not doing "OR cleaning" in my chains, because this expression has no logical meaning and is very confusing. While finding an nrc(z)(t)-chain from left to right, t- or z- candidates may not be "cleaned" (= "erased", "eliminated"). At each step, there is one and only one left-linking candidate and there is one and only one right-linking candidate. Exactly as in an xy-chain. There is never any form of OR branching. Additional t- or z- candidates are not "cleaned", their presence (which remains unchanged by the fact that one is finding a chain) may only be forgotten in the context of the previous candidates of this chain.

champagne wrote:UR is for sure Unique Rectangle. I see no reaon why ths should be excluded as a logic rule.

If you accept uniqueness, no problem. Just a matter of taste. This is not the main problem here.
But, in this case, I wouldn't claim I'm using only AICs.
And, if I'm using grouped AICs, I wouldn't claim I'm using "basic" AICs.

champagne wrote:I don't know why you are always suspecting others to use T&E.

I'm not suspecting others in general , but tagging algorithms that glue pieces of well known patterns in uncontrollable ways.
I don't know whether you need T&E in this particular case. I said that, if "OR cleaning" was a conclusion of type "not C1 or not C2" (where Ci are candidates), this amounts to T&E. You haven't yet defined "OR cleaning".

Now, you seem to say it amounts to disguised forms of nrczt-chains.
Can't it also amount to disguised forms of nrczt-nets?
In both cases, it'd be the proof that your algorithm does more than the rules you're explicitly using.

champagne wrote:I like density of "T" chains, but believe me, it's not so easy to check.

I believe you. But if you call them by their full name instead of introducing a confusing one, you'll have a chance of understanding that they are at the top of a hierarchy of increasing complexity, starting with xy-chains and hxy-chains in the 2D spaces and nrc-chains in the full nrc-space (BTW, nrc-chains ARE the really "basic" AICs).

champagne wrote:I chose to give intermediate positions not only because I am tagging, but also to facilitate decoding of the solution

If you split chains into pieces (supposing you really have chains), don't be surprised that you are suspected of using T&E: the hallmark of T&E is using a sequence of several rules for a single elimination.

If you want to be convincing, write your solution as a sequence of standard AICs, without all the tags and the extra glueing. Then, we'll see what types of chains you are really using and what their lengths are.

denis_berthier
2010 Supporter

Posts: 1377
Joined: 19 June 2007
Location: Paris

Just to convince Denis that this is 100% standard AICs, a translation of the first steps without any tag.

I also discarded UR to check that it has no influence on the ranking of that puzzle.

1 r9c9=2

-> column 7 digit 3 in box 3
-> row 2 digit 9 in box 1
XWing digit 4 columns 57 rows 37

Code: Select all
`1278 12478  1378  |3467 2368  5     |3689 4678  6789 6    24789  3789  |347  238   23478 |5    478   1    78   5      378   |1    3468  9     |3468 2     678  ----------------------------------------------------189  1689   5     |3469 7     348   |2    1368  689  3    126789 16789 |569  25689 28    |1689 1568  4    289  2689   4     |3569 1     238   |7    3568  5689 ----------------------------------------------------1578 3      178   |2    45    6     |148  9     578  4    16789  2     |579  59    17    |168  15678 3    1579 1679   1679  |8    359   1347  |16   14567 2 `

original chain translated
[]9r8c4 - 9r8c5 = 5r8c5 - 5r7c5 = 4r7c5 -4r3c5 = 4r3c7 - 3r3c7 = 3r1c7 - 9r1c7 = 9r5c7 - 9r5c5 = 9r89c5 -9r8c4

and the best chain should accept Denis
[] 9r8c5 = 5r8c5 - 5r7c5 = 4r7c5 -4r3c5 = 4r3c7 - 3r3c7 = 3r1c7 - 9r1c7 = 9r5c7
#9r8c4 #9r5c5

Code: Select all
`1278 12478  1378  |3467 2368 5     |3689 4678  6789 6    24789  3789  |347  238  23478 |5    478   1    78   5      378   |1    3468 9     |3468 2     678  ---------------------------------------------------189  1689   5     |3469 7    348   |2    1368  689  3    126789 16789 |569  2568 28    |1689 1568  4    289  2689   4     |3569 1    238   |7    3568  5689 ---------------------------------------------------1578 3      178   |2    45   6     |148  9     578  4    16789  2     |57   59   17    |168  15678 3    1579 1679   1679  |8    359  1347  |16   14567 2   `

Now these two chains
[]2r5c5.U - 5r5c5.Z = 7r2c6.z - 2r2c6.U
[]8r5c5.ë - 5r5c5.Z = 7r2c6.z - 8r2c6.ë

Denis should accept that equivalence

[]2r2c6 - 2r12c5 = 2r5c5 - 5r5c5 = 5r56c4 - 5r8c4 = 7r8c4 - 7r12c4 = 7r2c6

same final effect #2r5c5 #2r2c6 #8r5c5 #8r2c6

Code: Select all
`1278 12478  1378  |3467 2368 5    |3689 4678  6789 6    24789  3789  |347  238  347  |5    478   1    78   5      378   |1    3468 9    |3468 2     678  --------------------------------------------------189  1689   5     |3469 7    348  |2    1368  689  3    126789 16789 |569  56   28   |1689 1568  4    289  2689   4     |3569 1    238  |7    3568  5689 --------------------------------------------------1578 3      178   |2    45   6    |148  9     578  4    16789  2     |57   59   17   |168  15678 3    1579 1679   1679  |8    359  1347 |16   14567 2 `

[]1r9c7 = 6r9c7 - 6r9c3 = 6r5c3 - 6r5c5 = 5r8c5 - 5r56c4 = 5r8c4 - 5r7c5
= 4r7c5 - 4r7c7 = 4r3c7 - 3r3c7 = 3r1c7 - 9r1c7 = 9r5c7

#1r5c7

Code: Select all
`1278 12478  1378  |3467 2368 5    |3689 4678 6789 6    24789  3789  |347  238  347  |5    478  1    78   5      378   |1    3468 9    |3468 2    678  -------------------------------------------------189  1689   5     |3469 7    348  |2    1368 689  3    126789 16789 |569  56   28   |689  1568 4    289  2689   4     |3569 1    238  |7    3568 5689 -------------------------------------------------1578 3      178   |2    45   6    |148  9    578  4    16789  2     |57   59   17   |168  5678 3    1579 1679   1679  |8    359  1347 |16   4567 2  `

[]4r9c8 = 4r7c7 - 4r7c5 = 5r7c5 - 5r7c1 = 5r9c1
#5r9c8

Code: Select all
`1278 12478  1378  |3467 2368 5    |3689 4678 6789 6    24789  3789  |347  238  347  |5    478  1    78   5      378   |1    3468 9    |3468 2    678  -------------------------------------------------189  1689   5     |3469 7    348  |2    1368 689  3    126789 16789 |569  56   28   |689  1568 4    289  2689   4     |3569 1    238  |7    3568 5689 -------------------------------------------------1578 3      178   |2    45   6    |148  9    578  4    16789  2     |57   59   17   |168  5678 3    1579 1679   1679  |8    359  1347 |16   467  2 `

[]9r1c9 = 9r1c7 - 3r1c7 = 3r3c7 - 4r3c7 = 4r7c7 - 4r7c5 = 5r7c5 - 5r7c9 = 5r6c9 #9r6c1

[]9r1c9 = 9r1c7 - 3r1c7 = 3r3c7 - 4r3c7 = 4r7c7 - 4r7c5 = 5r7c5 - 5r8c4 = 5r56c4 - 5r5c5 = 6r5c5 - 6r13c5 =6r1c4
#6r1c9
[]9r5c7 = 9r1c7 - 3r1c7 = 3r3c7 - 4r3c7 = 4r7c7 - 4r7c5 = 5r7c5 - 5r8c4 = 5r56c4 - 5r5c5 = 6r5c5
#6r5c7
[]9r5c7 = 9r1c7 - 3r1c7 = 3r3c7 - 4r3c7 = 4r7c7 - 4r7c5 = 5r7c5 - 5r9c5 = 5r9c1 - 9r9c1 = 9r46c1
#9r5c23
[]4r9c8 = 4r7c7 - 4r7c5 = 5r7c5 - 5r8c4 = 5r56c4 - 5r5c5 = 6r5c5 - 6r5c3 = 6r9c3
#6r9c8

Translating is done very easily

champagne
2017 Supporter

Posts: 7033
Joined: 02 August 2007
Location: France Brittany

denis wrote

If you accept uniqueness, no problem. Just a matter of taste. This is not the main problem here.
But, in this case, I wouldn't claim I'm using only AICs.
And, if I'm using grouped AICs, I wouldn't claim I'm using "basic" AICs.

are you serious !!
champagne
2017 Supporter

Posts: 7033
Joined: 02 August 2007
Location: France Brittany

champagne wrote:denis wrote
If you accept uniqueness, no problem. Just a matter of taste. This is not the main problem here.
But, in this case, I wouldn't claim I'm using only AICs.
And, if I'm using grouped AICs, I wouldn't claim I'm using "basic" AICs.

are you serious !!

Unless you think words have no meaning.

And you've not yet answered my question about "OR cleaning" in general being a disguised form of I don't know what.
denis_berthier
2010 Supporter

Posts: 1377
Joined: 19 June 2007
Location: Paris

Denis wrote

And you've not yet answered my question about "OR cleaning" in general being a disguised form of I don't know what
.

"OR" cleaning in nothing else that the way an AIC ending with two strong links clears candidates. At least one of the end is true. This is a logical OR.

You express it as you want, most of the players see it as a "OR" and are looking for one of the patterns allowing clearance. This has been well described years ago by Bob Hansom

You shoul really have a look on what is written on that topic.

This is explained with a lot of details on my website (still a draft) with a plus for you, a french version.

Main entry for the site is here,

http://pagesperso-orange.fr/gpenet/

but I sugget you go here
http://pagesperso-orange.fr/gpenet/UM/UM00
for a general presentation

or may be here
http://pagesperso-orange.fr/gpenet/UM/UM00_fichiers/UO00.htm

to have a theoretical approach of the method

champagne
2017 Supporter

Posts: 7033
Joined: 02 August 2007
Location: France Brittany

I generally like to solve before I peak at other's solutions, so I have no clue if I am repeating the obvious below:

start 24 givens. (2)r9c9%box
1a) xwing 4 r37c57=> r129c5,r19c7<>4
1b) (5)r8c8=(5)r8c45-(5=4)r7c5-(4)r9c6=(4-57)r9c8=(hp57)r8c8r7c9 =>
r8c8<>168
1c) hp 68 r8c27 => (6=8)r8c27 => (1)r8c6

2a) Locked 9's r8c45 => r9c5<>9
2b) (9)r5c7=(9-3)r1c7=(3-4)r3c7=(4)r7c7-(4=5)r7c5-(5=9)r8c5 => r5c5<>9 => (9)r8c5

3a) (5) r8c4=r8c8-r7c9=r6c9 =>r6c4<>5
3b) (5)r5c4=(5)r8c4-(5=4)r7c5-(4)r3c5=(4-3)r3c7=(3-9)r1c7=(9)r5c7=> r5c4<>9
3c) (2)r56c6=(2-7)r2c6=(7)r9c6-(7=5)r8c4-(5)r5c4=(5)r5c5 => r5c5<>2
3d) (8)r456c6=(8-7)r2c6=(7)r9c6-(7=5)r8c4-(5)r5c4=(5)r5c5 => r5c5<>8
3e) pair 56 r5c45 => r2378c5,r46c4<>6, r5c8<>5
(6)r9c3%col,(6)r8c7%row,(1)r9c7%cell,(8)r8c2%cell

4)(9)r4c12=(9-4)r4c4=(4)r12c4-(4)r3c5=(4-3)r3c7=(3-9)r1c7=(9)r5c7 => r5c23<>9
(9)r5c7%row,r1c9%box,r3c2%column

5a) Locked 3's r46c8 => r12c8<>3
5b) (7): r8c8=r8c4-r9c6=r2c6 => r2c8<>7
5c) hidden pair 67 r1c8,r3c9 => r3c9<>8,r1c8<>48
5d) (8=6)r4c9-(6)r3c9=(6-4)r3c5=(4)r3c7-(4=8)r2c8 => r456c8<>8 =>
(1)r5c8%cell, (8)r2c8%column, (8)r7c7%column,(3)r1c7%cell, (4)r3c7%cell, (4)r9c8%col,
(4)r7c5%col,(3)r3c3%col

6a) (7): r3c1=r3c9-r7c9=r7c13 => r9c1<>7
6b) (8)r1c3=(8-7)r5c3=(7)r5c2-(7)r9c2=(7)r7c13-(7)r7c9=(7)r3c9-(7=8)r3c1 =>
r1c1<>8,r12c2<>7
6c) (2)r1c1=(2-8)r6c1=(8)r5c3-(8)r1c3=(8-2)r1c5=(2)r2c45 => r2c2<>2
Hidden & naked singles to end.
Max depth 5. Max complexity - almost hidden pair within AIC (once). Many repeated chain segments. Possibly too many steps.
Steve K

Posts: 98
Joined: 18 January 2007

Next