+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . 1 . | . . . |
| . 1 2 | 3 . 4 | 5 6 . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . 2 3 | . . . | 7 8 . |
| . 4 7 | . 6 . | 1 2 . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . 3 1 | 8 . 7 | 6 4 . |
| . 5 8 | . . . | 2 3 . |
+-------+-------+-------+
***** SudoRules version 13.7wter2 *****
.............1.....123.456...........23...78..47.6.12...........318.764..58...23.
nrc-chain[2] c8n5{r4 r7} - r8n5{c9 c5} ==> r4c5 <> 5
xyz-chain[3] r6c4{n9 n5} - r5c5{n5 n4} - r9c5{n4 n9} ==> r4c5 <> 9
naked-quads-in-a-block b5{r5c4 r5c5 r6c4 r5c6}{n1 n4 n9 n5} ==> r6c6 <> 9, r6c6 <> 5, r4c6 <> 9, r4c6 <> 5, r4c6 <> 1, r4c5 <> 4, r4c4 <> 9, r4c4 <> 5, r4c4 <> 4
interaction row r4 with block b6 ==> r5c9 <> 4
naked-quads-in-a-block b5{r5c4 r5c5 r6c4 r5c6}{n1 n4 n9 n5} ==> r4c4 <> 1
;;; A
hidden-single-in-row r4 ==> r4c1 = 1
even now, there is a full Jellyfish:
jellyfish-in-columns n9{c2 c8 c3 c7}{r7 r4 r2 r1} ==> r7c9 <> 9, r7c6 <> 9, r7c5 <> 9, r7c4 <> 9, r7c1 <> 9, r4c9 <> 9, r2c9 <> 9, r2c6 <> 9, r2c4 <> 9, r2c1 <> 9, r1c9 <> 9, r1c6 <> 9
nrc-chain[3] c6n9{r5 r9} - r9c5{n9 n4} - b5n4{r5c5 r5c4} ==> r5c4 <> 9
jellyfish-in-columns n9{c2 c8 c3 c7}{r7 r4 r2 r1} ==> r1c5 <> 9, r1c4 <> 9
singles
GRID 0 SOLVED. LEVEL = NRCZT4_0, MOST COMPLEX RULE = SHQ
495786312
376512894
812394567
189273456
623451789
547968123
264135978
931827645
758649231
***** SudoRules version 15b.1.8-B *****
.............1.....123.456...........23...78..47.6.12...........318.764..58...23.
26 givens and 222 candidates
whip[2] c8n5{r4 r7} - r8n5{c9 .} ==> r4c5 <> 5
whip[3] r6c4{n9 n5} - r5c5{n5 n4} - r9c5{n4 .} ==> r4c5 <> 9
;;; the following replace most of the NQ eliminations:
whip[4] b5n7{r4c4 r4c5} - b5n2{r4c5 r4c6} - b5n3{r4c6 r6c6} - b5n8{r6c6 .} ==> r4c4 <> 5
whip[4] b5n7{r4c4 r4c5} - b5n2{r4c5 r4c6} - b5n3{r4c6 r6c6} - b5n8{r6c6 .} ==> r4c4 <> 4
whip[4] b5n7{r4c4 r4c5} - b5n2{r4c5 r4c6} - b5n3{r4c6 r6c6} - b5n8{r6c6 .} ==> r4c4 <> 1
whip[4] b5n7{r4c4 r4c5} - b5n2{r4c5 r4c6} - b5n3{r4c6 r6c6} - b5n8{r6c6 .} ==> r4c4 <> 9
whip[4] b5n7{r4c5 r4c4} - b5n2{r4c4 r4c6} - b5n3{r4c6 r6c6} - b5n8{r6c6 .} ==> r4c5 <> 4
interaction row r4 with block b6 ==> r5c9 <> 4
whip[4] r6c4{n5 n9} - r5c6{n9 n1} - r5c4{n1 n4} - r5c5{n4 .} ==> r4c6 <> 5
whip[4] r6c4{n9 n5} - r5c6{n5 n1} - r5c4{n1 n4} - r5c5{n4 .} ==> r4c6 <> 9
whip[4] r6c4{n5 n9} - r5c6{n9 n1} - r5c4{n1 n4} - r5c5{n4 .} ==> r6c6 <> 5
whip[4] r6c4{n9 n5} - r5c6{n5 n1} - r5c4{n1 n4} - r5c5{n4 .} ==> r6c6 <> 9
;;; same situation as A, except that r4c6 <> 1 is not obtained
whip[5] b4n1{r4c1 r5c1} - r5n6{c1 c9} - b6n5{r5c9 r6c9} - r6c4{n5 n9} - r5n9{c4 .} ==> r4c1 <> 5
whip[5] b4n1{r4c1 r5c1} - r5n6{c1 c9} - b6n9{r5c9 r6c9} - r6c4{n9 n5} - r5n5{c4 .} ==> r4c1 <> 9
whip[5] r4n1{c1 c6} - b5n8{r4c6 r6c6} - b5n3{r6c6 r4c5} - b5n2{r4c5 r4c4} - b5n7{r4c4 .} ==> r4c1 <> 8
whip[6] r8c9{n9 n5} - c8n5{r7 r4} - c8n9{r4 r7} - c7n9{r7 r4} - c3n9{r4 r1} - c2n9{r2 .} ==> r2c9 <> 9
whip[6] r8c9{n9 n5} - c8n5{r7 r4} - c8n9{r4 r7} - c7n9{r7 r4} - c3n9{r4 r2} - c2n9{r1 .} ==> r1c9 <> 9
whip[6] r9c5{n9 n4} - r5c5{n4 n5} - r8n5{c5 c9} - b9n9{r8c9 r9c9} - b7n9{r9c1 r8c1} - r3n9{c1 .} ==> r7c5 <> 9
braid[6] b5n5{r5c4 r6c4} - r8c9{n5 n9} - r6n9{c4 c1} - r3n9{c1 c5} - r5c5{n5 n4} - r9c5{n9 .} ==> r5c9 <> 5
whip[7] r9c5{n4 n9} - r5c5{n9 n5} - r8n5{c5 c9} - r8n9{c9 c1} - r3n9{c1 c9} - r6n9{c9 c4} - r5n9{c4 .} ==> r7c5 <> 4
whip[7] r9c5{n9 n4} - r5c5{n4 n5} - r8n5{c5 c9} - r8n9{c9 c1} - r3n9{c1 c9} - r6n9{c9 c4} - r5n9{c4 .} ==> r1c5 <> 9
braid[7] r2c8{n7 n9} - r3c9{n9 n8} - c7n8{r2 r7} - c7n9{r7 r4} - r9n7{c9 c1} - r3c1{n7 n9} - b4n9{r6c1 .} ==> r1c9 <> 7
braid[7] r2c8{n7 n9} - r3c9{n9 n8} - c7n8{r2 r7} - c7n9{r7 r4} - r9n7{c9 c1} - r3c1{n7 n9} - b4n9{r6c1 .} ==> r2c9 <> 7
braid[7] r2c8{n7 n9} - r9n7{c1 c9} - r3c9{n7 n8} - c7n8{r1 r7} - c7n9{r1 r4} - r3c1{n7 n9} - b4n9{r6c1 .} ==> r2c1 <> 7
braid[7] r6c4{n5 n9} - r8c9{n5 n9} - r5n9{c4 c1} - r3n9{c1 c5} - r8n5{c9 c5} - r5c5{n5 n4} - r9c5{n9 .} ==> r6c9 <> 5
interaction block b6 with row r4 ==> r4c3 <> 5
interaction column c3 with block b1 ==> r1c1 <> 5
interaction column c3 with block b1 ==> r2c1 <> 5
whip[4] c1n5{r5 r6} - r6c4{n5 n9} - r5n9{c4 c9} - r5n6{c9 .} ==> r5c1 <> 1
hidden-single-in-a-block ==> r4c1 = 1
braid[10] b4n8{r4c2 r6c1} - r6n5{c1 c4} - c5n3{r4 r7} - r6n9{c4 c9} - r8c9{n9 n5} - c5n5{r8 r1} - c5n2{r1 r8} - c5n7{r1 r3} - r3c1{n7 n9} - r8n9{c9 .} ==> r4c5 <> 8
interaction column c5 with block b2 ==> r1c6 <> 8
interaction column c5 with block b2 ==> r2c6 <> 8
whip[7] b2n8{r1c5 r3c5} - c1n8{r3 r6} - r6n5{c1 c4} - r6n9{c4 c9} - r3n9{c9 c1} - r8n9{c1 c5} - r9n9{c6 .} ==> r1c2 <> 8
whip[8] b2n8{r1c5 r3c5} - c5n7{r3 r4} - c5n3{r4 r7} - c5n2{r7 r8} - r8c1{n2 n9} - r3n9{c1 c9} - r6n9{c9 c4} - r5n9{c4 .} ==> r1c5 <> 5
braid[5] r6n3{c9 c6} - c5n3{r4 r7} - r6c4{n9 n5} - r8c9{n9 n5} - c5n5{r8 .} ==> r6c9 <> 9
naked-single ==> r6c9 = 3
naked-single ==> r6c6 = 8
hidden-single-in-a-row ==> r4c2 = 8
whip[2] r6n9{c4 c1} - b7n9{r9c1 .} ==> r7c4 <> 9
whip[3] r6n9{c4 c1} - r8n9{c1 c9} - r3n9{c9 .} ==> r5c5 <> 9
whip[3] r9c5{n9 n4} - r5c5{n4 n5} - r6c4{n5 .} ==> r9c4 <> 9
whip[3] r6n9{c1 c4} - r5n9{c4 c9} - b9n9{r9c9 .} ==> r7c1 <> 9
whip[4] b4n9{r6c1 r4c3} - b6n9{r4c9 r5c9} - r8n9{c9 c5} - r3n9{c5 .} ==> r9c1 <> 9
whip[3] b7n9{r7c2 r8c1} - b4n9{r5c1 r4c3} - b6n9{r4c9 .} ==> r7c9 <> 9
whip[4] r9n9{c6 c9} - r8n9{c9 c1} - r5n9{c1 c4} - r6n9{c4 .} ==> r7c6 <> 9
whip[4] b8n9{r9c6 r8c5} - r3n9{c5 c1} - r6n9{c1 c4} - r5n9{c4 .} ==> r9c9 <> 9
interaction row r9 with block b8 ==> r8c5 <> 9
whip[2] r8n9{c9 c1} - b4n9{r5c1 .} ==> r4c9 <> 9
whip[3] r6n9{c4 c1} - r3n9{c1 c9} - r8n9{c9 .} ==> r1c4 <> 9
whip[3] r6n9{c4 c1} - r3n9{c1 c9} - r8n9{c9 .} ==> r2c4 <> 9
interaction column c4 with block b5 ==> r5c6 <> 9
whip[3] r6n9{c1 c4} - r5n9{c4 c9} - r8n9{c9 .} ==> r1c1 <> 9
whip[3] r6n9{c1 c4} - r5n9{c4 c9} - r8n9{c9 .} ==> r2c1 <> 9
whip[3] r6n9{c1 c4} - r5n9{c4 c9} - r8n9{c9 .} ==> r3c1 <> 9
whip[3] r8n9{c9 c1} - r5n9{c1 c4} - r6n9{c4 .} ==> r3c9 <> 9
singles
GRID 0 SOLVED. B = 10, MOST COMPLEX RULE = Braid[10]
495786312
376512894
812394567
189273456
623451789
547968123
264135978
931827645
758649231
***** SudoRules version 15b.1.12-GW *****
.............1.....123.456...........23...78..47.6.12...........318.764..58...23.
26 givens and 222 candidates
whip[2] c8n5{r4 r7} - r8n5{c9 .} ==> r4c5 <> 5
whip[3] r6c4{n9 n5} - r5c5{n5 n4} - r9c5{n4 .} ==> r4c5 <> 9
g-whip[3] b6n9{r4c7 r456c9} - r3n9{c9 c5} - r8n9{c5 .} ==> r4c1 <> 9
g-whip[3] b4n9{r4c3 r456c1} - r3n9{c1 c5} - r8n9{c5 .} ==> r4c9 <> 9
g-whip[3] b7n9{r7c3 r789c1} - r3n9{c1 c9} - b9n9{r9c9 .} ==> r7c5 <> 9
g-whip[3] b4n9{r6c1 r4c123} - b6n9{r4c7 r456c9} - b9n9{r9c9 .} ==> r7c1 <> 9
g-whip[3] b7n9{r7c3 r789c1} - r5n9{c1 c456} - r6n9{c6 .} ==> r7c9 <> 9
whip[4] b5n7{r4c4 r4c5} - b5n2{r4c5 r4c6} - b5n3{r4c6 r6c6} - b5n8{r6c6 .} ==> r4c4 <> 5
whip[4] b5n7{r4c4 r4c5} - b5n2{r4c5 r4c6} - b5n3{r4c6 r6c6} - b5n8{r6c6 .} ==> r4c4 <> 4
whip[4] b5n7{r4c4 r4c5} - b5n2{r4c5 r4c6} - b5n3{r4c6 r6c6} - b5n8{r6c6 .} ==> r4c4 <> 1
whip[4] b5n7{r4c4 r4c5} - b5n2{r4c5 r4c6} - b5n3{r4c6 r6c6} - b5n8{r6c6 .} ==> r4c4 <> 9
whip[4] b5n7{r4c5 r4c4} - b5n2{r4c4 r4c6} - b5n3{r4c6 r6c6} - b5n8{r6c6 .} ==> r4c5 <> 4
interaction row r4 with block b6 ==> r5c9 <> 4
whip[4] r6c4{n5 n9} - r5c6{n9 n1} - r5c4{n1 n4} - r5c5{n4 .} ==> r4c6 <> 5
whip[4] r6c4{n9 n5} - r5c6{n5 n1} - r5c4{n1 n4} - r5c5{n4 .} ==> r4c6 <> 9
whip[4] r6c4{n5 n9} - r5c6{n9 n1} - r5c4{n1 n4} - r5c5{n4 .} ==> r6c6 <> 5
whip[4] r6c4{n9 n5} - r5c6{n5 n1} - r5c4{n1 n4} - r5c5{n4 .} ==> r6c6 <> 9
g-whip[3] b9n9{r7c7 r789c9} - r6n9{c9 c1} - b7n9{r9c1 .} ==> r7c4 <> 9
g-whip[4] b4n9{r5c1 r4c123} - b6n9{r4c7 r456c9} - r8n9{c9 c5} - r9n9{c6 .} ==> r3c1 <> 9
whip[3] r3n9{c5 c9} - r8n9{c9 c1} - r6n9{c1 .} ==> r5c5 <> 9
whip[3] r9c5{n9 n4} - r5c5{n4 n5} - r6c4{n5 .} ==> r9c4 <> 9
whip[4] r9n7{c9 c1} - r3c1{n7 n8} - r3c9{n8 n9} - r2c8{n9 .} ==> r2c9 <> 7
whip[4] r9n7{c9 c1} - r3c1{n7 n8} - r3c9{n8 n9} - r2c8{n9 .} ==> r1c9 <> 7
whip[4] r2c8{n7 n9} - r3n9{c9 c5} - r3n7{c5 c9} - r9n7{c9 .} ==> r2c1 <> 7
whip[4] r8c9{n5 n9} - r3n9{c9 c5} - r9c5{n9 n4} - r5c5{n4 .} ==> r8c5 <> 5
singles ==> r8c9 = 5, r4c8 = 5
interaction column c3 with block b1 ==> r1c1 <> 5, r2c1 <> 5
whip[3] r8n9{c1 c5} - r9n9{c6 c9} - r3n9{c9 .} ==> r7c3 <> 9
whip[3] r8n9{c1 c5} - r9n9{c6 c9} - r3n9{c9 .} ==> r7c2 <> 9
interaction block b7 with column c1 ==> r1c1 <> 9, r2c1 <> 9, r5c1 <> 9, r6c1 <> 9
interaction block b4 with row r4 ==> r4c7 <> 9
interaction block b6 with column c9 ==> r9c9 <> 9
interaction block b9 with row r7 ==> r7c6 <> 9
interaction block b6 with column c9 ==> r1c9 <> 9, r2c9 <> 9, r3c9 <> 9
singles
GRID 0 SOLVED. GW = 4, MOST COMPLEX RULE = G-Whip[4]
495786312
376512894
812394567
189273456
623451789
547968123
264135978
931827645
758649231
[edit 04/05/2011: corrected a bug in my implementation of g-whips]
denis_berthier wrote:1) "normal" solution with subsets, NRCZT=4
...
- Code: Select all
***** SudoRules version 13.7wter2 *****
.............1.....123.456...........23...78..47.6.12...........318.764..58...23.
nrc-chain[2] c8n5{r4 r7} - r8n5{c9 c5} ==> r4c5 <> 5
xyz-chain[3] r6c4{n9 n5} - r5c5{n5 n4} - r9c5{n4 n9} ==> r4c5 <> 9
naked-quads-in-a-block b5{r5c4 r5c5 r6c4 r5c6}{n1 n4 n9 n5} ==> r6c6 <> 9, r6c6 <> 5, r4c6 <> 9, r4c6 <> 5, r4c6 <> 1, r4c5 <> 4, r4c4 <> 9, r4c4 <> 5, r4c4 <> 4
interaction row r4 with block b6 ==> r5c9 <> 4
naked-quads-in-a-block b5{r5c4 r5c5 r6c4 r5c6}{n1 n4 n9 n5} ==> r4c4 <> 1
;;; A
hidden-single-in-row r4 ==> r4c1 = 1
even now, there is a full Jellyfish:
jellyfish-in-columns n9{c2 c8 c3 c7}{r7 r4 r2 r1} ==> r7c9 <> 9, r7c6 <> 9, r7c5 <> 9, r7c4 <> 9, r7c1 <> 9, r4c9 <> 9, r2c9 <> 9, r2c6 <> 9, r2c4 <> 9, r2c1 <> 9, r1c9 <> 9, r1c6 <> 9
nrc-chain[3] c6n9{r5 r9} - r9c5{n9 n4} - b5n4{r5c5 r5c4} ==> r5c4 <> 9
jellyfish-in-columns n9{c2 c8 c3 c7}{r7 r4 r2 r1} ==> r1c5 <> 9, r1c4 <> 9
...
ronk wrote:I realize the "normal" solution is not the focus of your post, but why does the same "naked-quads-in-a-block b5" appear a second time? The elimination(s) made upon the 2nd appearance were available at the 1st.
Ditto for the 2nd appearance of "jellyfish-in-columns n9."
denis_berthier wrote:I've now coded g-braids in SudoRules. As for braids wrt whips, g-braids are much slower and more greedy for memory than g-whips.
For the same exceptional puzzle as above, I get GB = 4.
So, we finally have a whole range of ratings: NRCZT = 4, W > 18 , B = 10, GW = 6, GB = 4
- Code: Select all
***** SudoRules version 15b.1.11-GB *****
.............1.....123.456...........23...78..47.6.12...........318.764..58...23.
same path as with g-whips, down to: hidden-single-in-a-block ==> r4c1 = 1
...
g-whip[3] 9b7{r7c2 r789c1} - 9r6{c1 c9} - 9b9{r789c9 .} ==> r7c4 <> 9
Mauricio wrote:After following your solution up to hidden-single-in-a-block ==> r4c1 = 1
Mauricio wrote:xsudo reports (formatted by me)
- Code: Select all
g-whip[3] 9b7{r7c2 r789c1} - 9r6{c1 c9} - 9b9{r789c9 .} ==> r7c4 <> 9
denis_berthier wrote:Mauricio wrote:After following your solution up to hidden-single-in-a-block ==> r4c1 = 1
I can't check your sayings, as xsudo works only on windows. But I seriously doubt that xsudo follows the same path as SudoRules. So, could you please publish the complete exact xsudo output without any interpretation or reformatting?
About not allowing segments as llc's, is there a reason not to allow them? I remember you said once that allowing them does not increase the resolution power, but to me that claim is not clear.denis_berthier wrote:BTW, g-whips don't have segments as left linking candidates.
g-whip[3] 9b7{r7c2 r789c1} - 9r6{c1 c9} - 9b9{r9c9 .} ==> r7c4 <> 9
Mauricio wrote:I thought it was clear that I followed your solution path, and then I used xsudo to check what the next step was, not that xsudo followed your path right from step 1.
Mauricio wrote:About not allowing segments as llc's, is there a reason not to allow them? I remember you said once that allowing them does not increase the resolution power, but to me that claim is not clear.denis_berthier wrote:BTW, g-whips don't have segments as left linking candidates.
Mauricio wrote:let reword the whip
- Code: Select all
g-whip[3] 9b7{r7c2 r789c1} - 9r6{c1 c9} - 9b9{r9c9 .} ==> r7c4 <> 9
+-------------------------+-------------------------+-------------------------+
|x x x |x x x |x x x |
|x x x |x 1 x |x x x |
|x 1 2 |3 x 4 |5 6 x |
+-------------------------+-------------------------+-------------------------+
|x x x |1 x x |x x x |
|x 2 3 |x x x |7 8 x |
|589 4 7 |59 6 38 |1 2 359 |
+-------------------------+-------------------------+-------------------------+
|2467 679 469 |9? x x |89 1579 1578 |
|29 3 1 |8 x 7 |6 4 59 |
|4679 5 8 |x x x |2 3 179 |
+-------------------------+-------------------------+-------------------------+
denis_berthier wrote:For a better understanding, at the point, you're mentioning, the PM is (I filled only the relevant cells and 9? is the target):
3456789 6789 4569 | 25679 25789 25689 | 3489 179 1234789
3456789 6789 4569 | 25679 1 25689 | 3489 79 234789
789 1 2 | 3 789 4 | 5 6 789
-------------------------+-------------------------+------------------------
1 689 569 | 27 2378 238 | 349 59 3456
569 2 3 | 1459 459 159 | 7 8 569
589 4 7 | 59 6 38 | 1 2 359
-------------------------+-------------------------+------------------------
2467 679 469 | 124569 2345 123569 | 89 1579 1578
29 3 1 | 8 259 7 | 6 4 59
4679 5 8 | 1469 49 169 | 2 3 179
+-------+-------+-------+
| . . . | . . . | . . . |
| . 9 . | . 3 . | . 4 . |
| . . 2 | 6 . 1 | 5 . . |
+-------+-------+-------+
| . . 4 | . . . | 2 . . |
| . 3 . | . 5 . | . 1 . |
| . . 6 | . . . | 7 . . |
+-------+-------+-------+
| . . 5 | 8 . 2 | 6 . . |
| . 7 . | . 4 . | . 9 . |
| . . . | . . . | . . . |
+-------+-------+-------+
JasonLion wrote:I don't think you are using the word "anomaly" in the same way that most of us are when talking about SE. In SE land an "anomaly" is a rating that is inconsistent from the point of view of SEs definition, almost invariably because of a coding error in the SE code.
JasonLion wrote:Meanwhile I believe you are using "anomaly" to talk about inconsistencies with things outside the world of SE, of which there are many which are routinely ignored by users of SE.
JasonLion wrote:I find SE ratings interesting for two reasons that have nothing much to do with each other. First, SE ratings between about 1 and 7 correlate to the difficulty a human player might have solving the puzzle about as well as any single number rating system (ie they are all poor, and SE is no worse than any other).
JasonLion wrote:Second, SE ratings between about 9 and 12 seem to correlate fairly well with the computational complexity of producing puzzles. Producing puzzles with high SE ratings is far far more difficult than producing puzzles with lower ratings. While this correlation is also far from perfect, it seems to be far better than other available rating systems at rating the complexity of producing puzzles in this range.
denis_berthier wrote:As for the techniques SE uses in the puzzles rated above ~8 (which was the main question raised by my post), I'd like to believe I'm the only one that doesn't understand what all its types of "forcing chains" are (this is what is at stakes in the 8-12 range). But I fear I'm not. Even after scanning the whole SE cloning thread, I couldn't find any definition of them (nor any claim that they were clearly understood by anyone). At least, there was a positive result for me: I lost most of my initial interest in trying to understand them.