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This one has B-rating=29 and gB-rating=28, which surprises me, since I would think that the gB-rating would be a lot lower for difficult puzzles that the B-rating.

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001002003000010040500300100006007002010000080700900300007006008090040000300700500

gB solution: Show

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1)r2c7<>9, Braid[12]  {n9 n4}r4c7 - {n4 n2}r7c7 - n4{r6 r9}c9 - n9{r9 r5}c9 - n9r4{c8 c1} - n9r1{c1 c5} - n9{r3 r9}c6 - n1r9{c6 c8} - {n1 n5}r4c8 - n5r1{c8 c4} - {n5 n1}r7c4 - n1r4{c4 .}
2)r5c7<>9, gBraid[12]  {n9 n4}r4c7 - n9r4{c8 c1} - {n4 n2}r7c7 - n4{r6 r9}c9 - n9{r9 r123}c9 - n9r1{c8 c5} - n9{r3 r9}c6 - n1r9{c6 c8} - {n1 n5}r4c8 - n5r1{c8 c4} - {n5 n1}r7c4 - n1r4{c4 .}
3)r2c3<>2, gBraid[15]  n3r2{c3 c2} - n3{r2 r5}c3 - n7r2{c2 c789} - n9{r5 r3}c3 - n7{r3 r8}c8 - {n9 n6}r3c9 - {n6 n1}r8c9 - n1r9{c8 c6} - n1r6{c6 c8} - n6r6{c8 c5} - n6{r6 r9}c8 - n2r6{c5 c2} - {n6 n2}r8c7 - n2{r8 r7}c1 - n1r7{c1 .}
4)r4c2<>4, Braid[16]  {n4 n9}r4c7 - n3r4{c2 c5} - n3b4{r4c2 r5c3} - n3r7{c5 c8} - n9r5{c3 c1} - n9r7{c8 c5} - n9r1{c5 c8} - n9r9{c8 c9} - n4r9{c9 c3} - n4r3{c3 c6} - {n4 n5}r5c6 - n9r3{c6 c3} - {n9 n8}r2c3 - n8r3{c2 c5} - n7{r3 r1}c5 - n5{r1 .}c5
5)r2c3<>8, gBraid[16]  n3r2{c3 c2} - n3{r2 r5}c3 - n8{r2 r1}c7 - n7r2{c2 c789} - n9{r5 r3}c3 - n7{r3 r8}c8 - {n9 n6}r3c9 - {n6 n1}r8c9 - n1r9{c8 c6} - n1r6{c6 c8} - n9{r9 r2}c6 - n9r1{c5 c8} - {n9 n5}r4c8 - {n5 n8}r4c2 - n8r9{c2 c5} - n8{r8 .}c4
6)r7c8<>1, gBraid[28]  n1r4{c8 c4} - n3r7{c8 c5} - n1r9{c9 c6} - n1{r7 r8}c1 - n3{r7 r8}c8 - n9r7{c5 c7} - n3{r8 r5}c6 - n6b7{r8c1 r9c2} - n7{r8 r123}c8 - {n6 n2}r9c8 - n7r2{c9 c2} - n2{r8 r2}c7 - n8{r2 r1}c7 - {n8 n4}r1c2 - n4r3{c3 c6} - n4r7{c2 c1} - n4{r1 r5}c4 - n9{r3 r2}c6 - {n4 n8}r9c3 - n2{r7 r5}c1 - n2r6{c3 c5} - n6b5{r6c5 r5c5} - n6r3{c5 c789} - {n6 n5}r2c9 - n5r5{c9 c3} - {n5 n8}r6c2 - n8r3{c2 c5} - n8r4{c5 .}
7)r7c1<>4, Whip[4]  n1r7{c1 c4} - n1r4{c4 c8} - n1r9{c8 c9} - n4r9{c9 .}
8)r5c3<>4, Whip[10]  n4{r4 r1}c1 - n4{r1 r4}c4 - n1r4{c4 c8} - n1b5{r4c4 r6c6} - n1r9{c6 c9} - n4r9{c9 c2} - n6r9{c2 c8} - {n6 n5}r6c8 - n5b4{r6c3 r4c2} - n3b4{r4c2 .}
9)r1c7<>9, Braid[14]  {n9 n4}r4c7 - n8{r1 r2}c7 - {n4 n2}r7c7 - n4{r6 r9}c9 - {n2 n1}r7c1 - n9{r9 r5}c9 - {n1 n5}r7c4 - n9r4{c8 c1} - {n5 n6}r2c4 - {n6 n2}r2c1 - {n2 n4}r5c1 - {n4 n2}r5c4 - n2r8{c4 c3} - n5r8{c3 .}
10)r7c8<>2, gBraid[14]  {n2 n1}r7c1 - n2{r8 r2}c7 - n3{r7 r8}c8 - {n1 n5}r7c4 - n8{r2 r1}c7 - n7{r8 r123}c8 - {n5 n4}r7c2 - n7r2{c9 c2} - {n7 n6}r1c2 - {n6 n4}r1c4 - n6{r2 r8}c1 - n2{r8 r5}c1 - {n2 n6}r5c4 - n6{r5 .}c7
11)r8c6<>1, gBraid[10]  n1{r7 r4}c4 - n3{r8 r5}c6 - n3b8{r8c6 r7c5} - {n3 n9}r7c8 - n5b8{r7c5 r789c4} - {n9 n5}r4c8 - n5r1{c8 c5} - n9r1{c5 c1} - n5r5{c5 c3} - n9{r5 .}c3
12)r9c8<>1, Whip[2]  n1r4{c8 c4} - n1{r6 .}c6
13)r4c8<>9, gBraid[12]  {n9 n4}r4c7 - {n9 n3}r7c8 - n1r4{c8 c4} - n3r8{c8 c6} - n1{r6 r9}c6 - n9{r9 r123}c6 - n9r1{c5 c1} - {n9 n3}r2c3 - n4{r1 r5}c1 - {n4 n5}r5c6 - n5r4{c5 c2} - n3{r4 .}c2
14)r6c6<>8, Whip[7]  n1b5{r6c6 r4c4} - {n1 n5}r4c8 - {n5 n3}r4c5 - n3r5{c6 c3} - {n3 n9}r2c3 - {n9 n5}r2c6 - n5r1{c5 .}
15)r2c9<>6, Braid[8]  n5b3{r2c9 r1c8} - {n5 n1}r4c8 - {n1 n6}r6c8 - n6r9{c8 c2} - n6r3{c2 c5} - n6{r8 r1}c1 - n9r1{c1 c5} - n7{r1 .}c5
16)r6c6<>5, gBraid[10]  n1{r6 r9}c6 - n1b5{r6c6 r4c4} - {n1 n5}r4c8 - n5r5{c9 c3} - n5r8{c3 c4} - n3b4{r5c3 r4c2} - {n3 n8}r4c5 - n8b8{r9c5 r8c6} - n8r3{c6 c123} - n8{r2 .}c1
17)r7c5<>5, Braid[9]  n3r7{c5 c8} - n9r7{c8 c7} - n4b9{r7c7 r9c9} - n1r9{c9 c6} - {n1 n4}r6c6 - n1{r8 r4}c4 - {n1 n5}r4c8 - n5r1{c8 c4} - n4{r1 .}c4
18)r4c4<>5, gWhip[8]  n5{r6 r1}c5 - n5r2{c6 c9} - n5r5{c9 c3} - n9{r5 r123}c3 - n9r1{c1 c8} - {n9 n3}r7c8 - n3r8{c8 c6} - n5r8{c6 .}
19)r2c2<>6, gBraid[9]  n6{r1 r8}c1 - n7r2{c2 c789} - n7{r3 r8}c8 - {n7 n1}r8c9 - n3r8{c8 c6} - n1r9{c9 c6} - n8{r9 r123}c6 - {n8 n5}r2c4 - n5b8{r8c4 .}
20)r4c2<>8, Braid[9]  n3r4{c2 c5} - n8r6{c3 c5} - n3{r4 r2}c2 - n5r4{c5 c8} - {n3 n9}r2c3 - n5{r6 r2}c9 - {n5 n8}r2c6 - n8r3{c6 c3} - n8r9{c3 .}
21)r8c6<>8, Braid[9]  n3{r8 r5}c6 - n5{r5 r2}c6 - n5r1{c5 c8} - {n5 n1}r4c8 - {n1 n6}r6c8 - n1r6{c9 c6} - {n1 n9}r9c6 - {n9 n2}r9c5 - {n2 .}r9c8
22)r8c8<>1, gBraid[9]  {n1 n5}r4c8 - n3r8{c8 c6} - {n5 n3}r4c2 - {n5 n6}r6c8 - n5b8{r8c6 r789c4} - n5r1{c4 c5} - n7{r1 r3}c5 - n6{r3 r5}c5 - n3r5{c5 .}
23)r456c8==1
24)r9c9<>6, Whip[5]  n1r9{c9 c6} - {n1 n4}r6c6 - {n4 n5}r6c9 - {n5 n1}r4c8 - n1r6{c8 .}
25)r1c8<>6, Braid[9]  n6r9{c8 c2} - n6r3{c2 c5} - n6r6{c5 c9} - n7{r3 r1}c5 - {n7 n8}r1c7 - {n8 n4}r1c2 - n4r3{c3 c6} - n4r6{c6 c3} - n4{r5 .}c1
26)r5c4<>5, Braid[9]  n5r7{c4 c2} - n5r4{c2 c8} - n1r4{c8 c4} - {n1 n2}r7c4 - n1{r6 r9}c6 - {n2 n8}r8c4 - {n8 n9}r9c5 - {n9 n4}r9c9 - n4r7{c7 .}
27)r9c9<>9, Whip[9]  n1r9{c9 c6} - {n1 n4}r6c6 - n1r6{c6 c8} - {n1 n5}r4c8 - {n5 n6}r6c9 - {n6 n7}r3c9 - n7{r3 r1}c5 - n5r1{c5 c4} - n4{r1 .}c4
28)r3c8<>9, Braid[6]  n9{r2 r5}c9 - {n9 n4}r4c7 - n9{r5 r2}c3 - n9{r2 r9}c6 - n1r9{c6 c9} - n4{r9 .}c9
29)r1c7<>7, gWhip[8]  n7r5{c7 c9} - n9{r5 r123}c9 - {n9 n5}r1c8 - {n5 n1}r4c8 - n1r6{c8 c6} - n1r9{c6 c9} - n4{r9 r6}c9 - n5{r6 .}c9
30)r1c5<>8, Braid[7]  {n8 n6}r1c7 - n7{r1 r3}c5 - n6r3{c5 c2} - n8r3{c2 c3} - n8r6{c3 c2} - n8{r4 r8}c1 - n6{r8 .}c1
31)r2c7<>7, gWhip[8]  n7r5{c7 c9} - n9{r5 r123}c9 - {n9 n5}r1c8 - {n5 n1}r4c8 - n1r6{c8 c6} - n1r9{c6 c9} - n4{r9 r6}c9 - n5{r6 .}c9
32)r1c8<>9, gWhip[7]  {n9 n3}r7c8 - n3r8{c8 c6} - n5b8{r8c6 r789c4} - n5r1{c4 c5} - n7r1{c5 c2} - n7r2{c2 c9} - n5r2{c9 .}
33)r789c8==9
34) r4c7==9,  n9{. r4}c7
35)r7c5<>2, Whip[2]  n3r7{c5 c8} - n9r7{c8 .}
36)r2c2<>3, Whip[4]  {n3 n9}r2c3 - n9r1{c1 c5} - {n9 n3}r7c5 - n3r4{c5 .}
37) r2c3==3,  n3r2{. c3}
38) r4c2==3,  n3{. r4}c2
39)r6c5<>5, Braid[4]  n5b4{r6c3 r5c3} - n9{r5 r3}c3 - n5{r5 r2}c9 - n9{r2 .}c9
40)r6c8<>5, Whip[4]  n5{r5 r2}c9 - n9{r2 r3}c9 - n9{r3 r5}c3 - n5b4{r5c3 .}
41)r1c4<>5, Whip[4]  n5{r1 r4}c8 - n1r4{c8 c4} - {n1 n4}r6c6 - n4{r5 .}c4
42)r5c5<>5, Whip[2]  n5r1{c5 c8} - n5r4{c8 .}
43)r5c7<>6, Braid[4]  {n6 n1}r6c8 - {n1 n5}r4c8 - {n1 n4}r6c6 - {n4 .}r6c9
44)r5c9<>6, Braid[4]  {n6 n1}r6c8 - {n1 n5}r4c8 - {n1 n4}r6c6 - {n4 .}r6c9
45)r5c456==6
46)r1c5<>5, Whip[4]  n7{r1 r3}c5 - n6{r3 r5}c5 - n3r5{c5 c6} - n5b5{r5c6 .}
47) r1c8==5,  n5r1{. c8}
48) r4c8==1,  {. n1}r4c8
49) r6c8==6,  {. n6}r6c8
50) r4c5==5,  n5r4{. c5}
51) r6c6==1,  n1r6{. c6}
52) r9c9==1,  n1r9{. c9}
53) r9c2==6,  n6r9{. c2}
54) r9c3==4,  n4r9{. c3}
55) r7c7==4,  n4r7{. c7}
56) r5c7==7,  {. n7}r5c7
57)r9c456==8
58)r3c5<>7, Whip[3]  n6r3{c5 c9} - {n6 n7}r8c9 - n7{r8 .}c8
59) r1c5==7,  n7{. r1}c5
60) r1c1==9,  n9r1{. c1}
61) r5c3==9,  n9r5{. c3}
62) r5c9==5,  n5r5{. c9}
63) r6c9==4,  {. n4}r6c9
64) r2c1==6,  n6{. r2}c1
65)r1c2<>8, Whip[3]  {n8 n2}r3c3 - n2r2{c2 c7} - n8{r2 .}c7
66) r1c2==4,  {. n4}r1c2
67) r3c6==4,  n4r3{. c6}
68) r5c6==3,  {. n3}r5c6
69) r8c6==5,  {. n5}r8c6
70) r2c4==5,  n5r2{. c4}
71) r7c2==5,  n5r7{. c2}
72) r6c3==5,  n5r6{. c3}
73) r8c8==3,  n3r8{. c8}
74) r7c8==9,  {. n9}r7c8
75) r7c5==3,  {. n3}r7c5
76) r9c8==2,  {. n2}r9c8
77) r3c8==7,  {. n7}r3c8
78) r2c9==9,  {. n9}r2c9
79) r2c6==8,  {. n8}r2c6
80) r1c4==6,  {. n6}r1c4
81) r1c7==8,  {. n8}r1c7
82) r2c7==2,  {. n2}r2c7
83) r2c2==7,  {. n7}r2c2
84) r3c5==9,  {. n9}r3c5
85) r3c9==6,  {. n6}r3c9
86) r8c7==6,  {. n6}r8c7
87) r8c9==7,  {. n7}r8c9
88) r9c5==8,  {. n8}r9c5
89) r6c5==2,  {. n2}r6c5
90) r5c4==4,  {. n4}r5c4
91) r4c4==8,  {. n8}r4c4
92) r4c1==4,  {. n4}r4c1
93) r5c1==2,  {. n2}r5c1
94) r5c5==6,  {. n6}r5c5
95) r6c2==8,  {. n8}r6c2
96) r3c2==2,  {. n2}r3c2
97) r3c3==8,  {. n8}r3c3
98) r7c1==1,  {. n1}r7c1
99) r7c4==2,  {. n2}r7c4
100) r8c1==8,  {. n8}r8c1
101) r8c3==2,  {. n2}r8c3
102) r8c4==1,  {. n1}r8c4
103) r9c6==9,  {. n9}r9c6
Most difficult rule: gBraid[28]
Time elapsed: 2220.706 seconds

The solution path obtained by my rough Braid for this puzzle is as follows:

Hidden Text: Show

Code: Select all

Braid[12]: => r2c7<>9
9r2c7 - r4c7{n9=n4} - r7c7{n4=n2} - 4b9{r7c7=r9c9} - 9c9{r9c9=r5c9} - 9b4{r5c1=r4c1} - 9r1{r1c1=r1c5} - 9b8{r7c5=r9c6} - 1r9{r9c6=r9c8} - r4c8{n1=n5} - 1r4{r4c8=r4c4} - r7c4{n1=n5} - 5r1{r1c4=.}
g-Braid[12]: => r5c7<>9
9r5c7 - r4c7{n9=n4} - 9b4{r5c1=r4c1} - r7c7{n4=n2} - 4b9{r7c7=r9c9} - 9b9{r9c9=r79c8} - 9r1{r1c8=r1c5} - 9b8{r7c5=r9c6} - 1r9{r9c6=r9c8} - r4c8{n1=n5} - 1r4{r4c8=r4c4} - r7c4{n1=n5} - 5r1{r1c4=.}
g-Braid[15]: => r2c3<>2
2r2c3 - 3b1{r2c3=r2c2} - 3b4{r4c2=r5c3} - 7r2{r2c2=r2c79} - 9c3{r5c3=r3c3} - 7c8{r1c8=r8c8} - r3c9{n9=n6} - r8c9{n6=n1} - 1b7{r8c1=r7c1} - 1b8{r7c4=r9c6} - 1r6{r6c6=r6c8} - 6b6{r6c8=r5c7} - r8c7{n6=n2} - 2c1{r8c1=r5c1} - 2b5{r5c4=r6c5} - 6r6{r6c5=.}
g-Braid[16]: => r4c2<>4
4r4c2 - r4c7{n4=n9} - 3b4{r4c2=r5c3} - r4c1{n9=n8} - 3c6{r5c6=r8c6} - 3b9{r8c8=r7c8} - 9r7{r7c8=r7c5} - 5b8{r7c5=r78c4} - r4c4{n5=n1} - 1r7{r7c4=r7c1} - 4b7{r7c1=r9c3} - 4r3{r3c3=r3c6} - 9b2{r3c6=r2c6} - r2c3{n9=n8} - r2c4{n8=n6} - r1c4{n6=n8} - 8r3{r3c5=.}
g-Braid[16]: => r2c3<>8
8r2c3 - 3b1{r2c3=r2c2} - 3b4{r4c2=r5c3} - 8b3{r2c7=r1c7} - 7r2{r2c2=r2c79} - 9c3{r5c3=r3c3} - 7c8{r1c8=r8c8} - r3c9{n9=n6} - r8c9{n6=n1} - 1r9{r9c8=r9c6} - 1b5{r6c6=r4c4} - 8c4{r4c4=r8c4} - 8b7{r8c1=r9c2} - r4c2{n8=n5} - r4c8{n5=n9} - 9b3{r1c8=r2c9} - 9c6{r2c6=.}
g-Braid[28]: => r7c8<>1
1r7c8 - 1b7{r7c1=r8c1} - 1b6{r4c8=r6c9} - 1b8{r8c4=r9c6} - 1b5{r6c6=r4c4} - 3b9{r7c8=r8c8} - 3b8{r8c6=r7c5} - 6b7{r8c1=r9c2} - 7c8{r8c8=r13c8} - 9r7{r7c5=r7c7} - 7r2{r2c7=r2c2} - r9c8{n9=n2} - 2b3{r3c8=r2c7} - 8b3{r2c7=r1c7} - r1c2{n8=n4} - 4b2{r1c4=r3c6} - 4r7{r7c2=r7c1} - 4b5{r5c6=r5c4} - 2c1{r7c1=r5c1} - 9c6{r3c6=r2c6} - 2b5{r5c5=r6c5} - 6r6{r6c5=r6c8} - 6b5{r6c5=r5c5} - 6r3{r3c5=r3c9} - 9c9{r3c9=r5c9} - r4c8{n9=n5} - r4c5{n5=n8} - 8b2{r3c5=r2c4} - 8c1{r2c1=.}
Whip[4]: => r7c1<>4
4r7c1 - 1r7{r7c1=r7c4} - 1r4{r4c4=r4c8} - 1r9{r9c8=r9c9} - 4r9{r9c9=.}
g-Braid[10]: => r5c3<>4
4r5c3 - 3b4{r5c3=r4c2} - 4c1{r4c1=r1c1} - 5b4{r4c2=r6c23} - 4c4{r1c4=r4c4} - 1b5{r4c4=r6c6} - 1b6{r6c8=r4c8} - 1r9{r9c8=r9c9} - r6c8{n1=n6} - 6r9{r9c8=r9c2} - 4r9{r9c2=.}
g-Braid[14]: => r7c8<>2
2r7c8 - r7c1{n2=n1} - 2b3{r3c8=r2c7} - 3b9{r7c8=r8c8} - r7c4{n1=n5} - 8b3{r2c7=r1c7} - 7c8{r8c8=r13c8} - r7c2{n5=n4} - 7r2{r2c9=r2c2} - r1c2{n7=n6} - r1c4{n6=n4} - 6b7{r9c2=r8c1} - 2c1{r8c1=r5c1} - r5c4{n2=n6} - 6c7{r5c7=.}
g-Braid[13]: => r8c6<>1
1r8c6 - 1b5{r6c6=r4c4} - 3b8{r8c6=r7c5} - 3b5{r4c5=r5c6} - r7c8{n3=n9} - 5b8{r7c5=r78c4} - r4c8{n9=n5} - 5r1{r1c8=r1c5} - 5r5{r5c5=r5c3} - 5b7{r8c3=r7c2} - 4r7{r7c2=r7c7} - r4c7{n4=n9} - 9b4{r4c1=r5c1} - 9r1{r1c1=.}
Whip[2]: => r9c8<>1
1r9c8 - 1b6{r4c8=r6c9} - 1c6{r6c6=.}
g-Braid[13]: => r4c8<>9
9r4c8 - r4c7{n9=n4} - r7c8{n9=n3} - 4b9{r7c7=r9c9} - 1r9{r9c9=r9c6} - 9b9{r9c9=r7c7} - 9b8{r7c5=r9c5} - 9r1{r1c5=r1c1} - r2c3{n9=n3} - 3b4{r5c3=r4c2} - 5r4{r4c2=r4c45} - 3c5{r4c5=r5c5} - r5c6{n3=n4} - 4c1{r5c1=.}
Whip[7]: => r6c6<>8
8r6c6 - 1b5{r6c6=r4c4} - r4c8{n1=n5} - r4c5{n5=n3} - 3b4{r4c2=r5c3} - r2c3{n3=n9} - r2c6{n9=n5} - 5r1{r1c4=.}
g-Braid[10]: => r6c6<>5
5r6c6 - 1b5{r6c6=r4c4} - 1b8{r7c4=r9c6} - r4c8{n1=n5} - 5b4{r4c2=r5c3} - 3b4{r5c3=r4c2} - 5r8{r8c3=r8c4} - r4c5{n3=n8} - 8b8{r9c5=r8c6} - 8c1{r8c1=r12c1} - 8r3{r3c2=.}
Braid[9]: => r7c5<>5
5r7c5 - 3r7{r7c5=r7c8} - 9r7{r7c8=r7c7} - 4b9{r7c7=r9c9} - 1r9{r9c9=r9c6} - r6c6{n1=n4} - 1b5{r6c6=r4c4} - r4c8{n1=n5} - 5r1{r1c8=r1c4} - 4c4{r1c4=.}
g-Braid[9]: => r2c2<>6
6r2c2 - 6b7{r9c2=r8c1} - 7r2{r2c2=r2c79} - 7c8{r1c8=r8c8} - 3r8{r8c8=r8c6} - r8c9{n7=n1} - 1r9{r9c9=r9c6} - 8c6{r9c6=r23c6} - r2c4{n8=n5} - 5b8{r7c4=.}
Braid[9]: => r8c6<>8
8r8c6 - 3c6{r8c6=r5c6} - 5c6{r5c6=r2c6} - 5b3{r2c9=r1c8} - r4c8{n5=n1} - r6c8{n1=n6} - 1b5{r4c4=r6c6} - r9c6{n1=n9} - r9c5{n9=n2} - r9c8{n2=.}
g-Whip[9]: => r1c7<>9
9r1c7 - r4c7{n9=n4} - 4b9{r7c7=r9c9} - 1r9{r9c9=r9c6} - r6c6{n1=n4} - 4c3{r6c3=r3c3} - 9b1{r3c3=r2c13} - 9c6{r2c6=r3c6} - 8c6{r3c6=r2c6} - 8c7{r2c7=.}
Braid[8]: => r4c4<>5
5r4c4 - 5b8{r7c4=r8c6} - 3b8{r8c6=r7c5} - 5r2{r2c6=r2c9} - r7c8{n3=n9} - 5r5{r5c9=r5c3} - 9b3{r1c8=r3c9} - 9c3{r3c3=r2c3} - 3c3{r2c3=.}
Whip[8]: => r2c9<>6
6r2c9 - 5b3{r2c9=r1c8} - r4c8{n5=n1} - r6c8{n1=n6} - 6b9{r8c8=r8c7} - 6c1{r8c1=r1c1} - 6b2{r1c4=r3c5} - 7b2{r3c5=r1c5} - 9r1{r1c5=.}
Braid[9]: => r4c2<>8
8r4c2 - 3b4{r4c2=r5c3} - 3b5{r5c5=r4c5} - r2c3{n3=n9} - 5r4{r4c5=r4c8} - 5b3{r1c8=r2c9} - r2c6{n5=n8} - 8b3{r2c7=r1c7} - 8c4{r1c4=r8c4} - 8c1{r8c1=.}
g-Braid[9]: => r8c8<>1
1r8c8 - r4c8{n1=n5} - 3r8{r8c8=r8c6} - r4c2{n5=n3} - r6c8{n5=n6} - 5b8{r8c6=r78c4} - 3b5{r4c5=r5c5} - 5r1{r1c4=r1c5} - 6c5{r1c5=r3c5} - 7c5{r3c5=.}
Whip[1]: => r6c9<>1
1r6c9 - 1c8{r4c8=.}
Whip[5]: => r9c9<>6
6r9c9 - 1r9{r9c9=r9c6} - r6c6{n1=n4} - r6c9{n4=n5} - r4c8{n5=n1} - 1r6{r6c8=.}
Braid[9]: => r5c4<>5
5r5c4 - 5b8{r7c4=r8c6} - 5b7{r8c3=r7c2} - 3b8{r8c6=r7c5} - 4r7{r7c2=r7c7} - r7c8{n3=n9} - r9c9{n9=n1} - 1c6{r9c6=r6c6} - 1b6{r6c8=r4c8} - 5r4{r4c8=.}
Braid[9]: => r9c9<>9
9r9c9 - 1r9{r9c9=r9c6} - r6c6{n1=n4} - 1b5{r6c6=r4c4} - r4c8{n1=n5} - r6c9{n5=n6} - r3c9{n6=n7} - 7b2{r3c5=r1c5} - 5r1{r1c5=r1c4} - 4c4{r1c4=.}
Whip[6]: => r3c8<>9
9r3c8 - 9b9{r7c8=r7c7} - 4b9{r7c7=r9c9} - 1r9{r9c9=r9c6} - 9b8{r9c6=r9c5} - 9r1{r1c5=r1c1} - 9r4{r4c1=.}
g-Braid[9]: => r1c8<>9
9r1c8 - r7c8{n9=n3} - 5b3{r1c8=r2c9} - 3b8{r7c5=r8c6} - 5b8{r8c6=r78c4} - 5b2{r1c4=r1c5} - 7b2{r1c5=r3c5} - 7c8{r3c8=r8c8} - 7c9{r8c9=r5c9} - 9c9{r5c9=.}
Whip[1]: => r5c9<>9
9r5c9 - 9b3{r2c9=.}
Hidden Single: 9 in b6 => r4c7=9
Whip[2]: => r7c5<>2
2r7c5 - 3r7{r7c5=r7c8} - 9r7{r7c8=.}
Braid[4]: => r2c2<>3
3r2c2 - r2c3{n3=n9} - 3r4{r4c2=r4c5} - r7c5{n3=n9} - 9r1{r1c5=.}
Hidden Single: 3 in r2 => r2c3=3
Hidden Single: 3 in c2 => r4c2=3
Whip[4]: => r6c5<>5
5r6c5 - 5b4{r6c2=r5c3} - 5c9{r5c9=r2c9} - 9b3{r2c9=r3c9} - 9c3{r3c3=.}
Braid[4]: => r6c8<>5
5r6c8 - 5b4{r6c2=r5c3} - 5b3{r1c8=r2c9} - 9b3{r2c9=r3c9} - 9c3{r3c3=.}
Whip[4]: => r1c4<>5
5r1c4 - 4b2{r1c4=r3c6} - r6c6{n4=n1} - 1b6{r6c8=r4c8} - 5c8{r4c8=.}
Whip[2]: => r5c5<>5
5r5c5 - 5r4{r4c5=r4c8} - 5r1{r1c8=.}
Braid[4]: => r1c8<>6
6r1c8 - 5r1{r1c8=r1c5} - 6r9{r9c8=r9c2} - 6r3{r3c2=r3c5} - 7c5{r3c5=.}
Braid[4]: => r5c7<>6
6r5c7 - r6c8{n6=n1} - r4c8{n1=n5} - r6c6{n1=n4} - r6c9{n4=.}
Braid[4]: => r5c9<>6
6r5c9 - r6c8{n6=n1} - r4c8{n1=n5} - r6c6{n1=n4} - r6c9{n4=.}
Whip[1]: => r6c5<>6
6r6c5 - 6r5{r5c4=.}
Whip[4]: => r1c5<>5
5r1c5 - 5b5{r4c5=r5c6} - 3b5{r5c6=r5c5} - 6c5{r5c5=r3c5} - 7c5{r3c5=.}
Hidden Single: 5 in r1 => r1c8=5
Hidden Single: 5 in r4 => r4c5=5
Naked Single: r4c8=1
Hidden Single: 1 in r6 => r6c6=1
Hidden Single: 1 in r9 => r9c9=1
Hidden Single: 4 in b9 => r7c7=4
Naked Single: r5c7=7
Naked Single: r6c8=6
Hidden Single: 6 in r9 => r9c2=6
Hidden Single: 4 in r9 => r9c3=4
Whip[1]: => r8c4<>8
8r8c4 - 8r9{r9c5=.}
Whip[3]: => r1c5<>8
8r1c5 - r1c7{n8=n6} - 6r3{r3c9=r3c5} - 7c5{r3c5=.}
Whip[3]: => r3c5<>7
7r3c5 - 6r3{r3c5=r3c9} - r8c9{n6=n7} - 7c8{r8c8=.}
Hidden Single: 7 in c5 => r1c5=7
Hidden Single: 9 in r1 => r1c1=9
Hidden Single: 9 in r5 => r5c3=9
Hidden Single: 5 in r5 => r5c9=5
Full House: r6c9=4
Hidden Single: 6 in c1 => r2c1=6
Whip[3]: => r1c2<>8
8r1c2 - r3c3{n8=n2} - 2b3{r3c8=r2c7} - 8c7{r2c7=.}
Naked Single: r1c2=4
Hidden Single: 4 in r3 => r3c6=4
Naked Single: r5c6=3
Hidden Single: 3 in r8 => r8c8=3
Hidden Single: 3 in r7 => r7c5=3
Hidden Single: 9 in r7 => r7c8=9
Hidden Single: 7 in r8 => r8c9=7
Hidden Single: 7 in r2 => r2c2=7
Hidden Single: 2 in r2 => r2c7=2
Hidden Single: 7 in r3 => r3c8=7
Full House: r9c8=2
Full House: r8c7=6
Full House: r1c7=8
Full House: r1c4=6
Hidden Single: 6 in r3 => r3c9=6
Full House: r2c9=9
Hidden Single: 9 in r3 => r3c5=9
Hidden Single: 6 in r5 => r5c5=6
Hidden Single: 9 in r9 => r9c6=9
Full House: r9c5=8
Full House: r6c5=2
Hidden Single: 2 in r5 => r5c1=2
Full House: r5c4=4
Full House: r4c4=8
Full House: r4c1=4
Hidden Single: 8 in r2 => r2c6=8
Full House: r2c4=5
Full House: r8c6=5
Hidden Single: 5 in r7 => r7c2=5
Hidden Single: 5 in r6 => r6c3=5
Full House: r6c2=8
Full House: r3c2=2
Full House: r3c3=8
Full House: r8c3=2
Hidden Single: 2 in r7 => r7c4=2
Full House: r7c1=1
Full House: r8c1=8
Full House: r8c4=1
gBraid[28] 101 Steps! Time elapsed: 18855.4 ms


[denis_berthier]

This one has B-rating=29 and gB-rating=28, which surprises me, since I would think that the gB-rating would be a lot lower for difficult puzzles that the B-rating.

The only thing we know is, in unbiased stats, W=gW=B=gB for 99.5% of the puzzles - but the mean values are quite low.
Puzzles with so high ratings have probability close to 0 and we know strictly nothing about the difference of their ratings.

[yzfwsf]

#153 from Top 1465, ER=4.0, But this puzzle cannot be solved by a whip or even a braid alone. It can be solved with gWhip[9] or gBaid[8]. Mauricio's js solver give rating gBraid[12].

Code: Select all

.9.....2...5..4.......61.....6...1.8...3...7.......6..23.9.........8.4..7........

Hidden Text: Show

Code: Select all

Hidden Single: 6 in r5 => r5c6=6
Hidden Single: 9 in b2 => r2c5=9
Whip[1]: => r1c1<>3
3r1c1 - 3b2{r1c5=.}
Whip[1]: => r1c3<>3
3r1c3 - 3b2{r1c5=.}
Whip[1]: => r1c7<>3
3r1c7 - 3b2{r1c5=.}
Whip[1]: => r1c9<>3
3r1c9 - 3b2{r1c5=.}
Whip[1]: => r4c4<>2
2r4c4 - 2b2{r2c4=.}
Whip[1]: => r6c1<>8
8r6c1 - 8r5{r5c1=.}
Whip[1]: => r6c2<>8
8r6c2 - 8r5{r5c1=.}
Whip[1]: => r6c3<>8
8r6c3 - 8r5{r5c1=.}
Whip[1]: => r6c4<>2
2r6c4 - 2b2{r2c4=.}
Whip[1]: => r8c4<>2
2r8c4 - 2b2{r2c4=.}
Whip[1]: => r8c8<>6
6r8c8 - 6r7{r7c8=.}
Whip[1]: => r8c9<>6
6r8c9 - 6r7{r7c8=.}
Whip[1]: => r9c4<>2
2r9c4 - 2b2{r2c4=.}
Whip[1]: => r9c8<>6
6r9c8 - 6r7{r7c8=.}
Whip[1]: => r9c9<>6
6r9c9 - 6r7{r7c8=.}
Whip[2]: => r3c8<>3
3r3c8 - 3b6{r4c8=r6c9} - 3c3{r6c3=.}
Braid[3]: => r8c6<>5
5r8c6 - r7c6{n5=n7} - 2r8{r8c6=r8c9} - 7r8{r8c9=.}
Whip[3]: => r1c1<>8
8r1c1 - 6r1{r1c1=r1c9} - 1r1{r1c9=r1c3} - 4r1{r1c3=.}
Whip[3]: => r1c9<>5
5r1c9 - 6r1{r1c9=r1c1} - 1r1{r1c1=r1c3} - 4r1{r1c3=.}
Whip[3]: => r1c9<>7
7r1c9 - 6r1{r1c9=r1c1} - 1r1{r1c1=r1c3} - 4r1{r1c3=.}
Braid[5]: => r3c3<>4
4r3c3 - 3c3{r3c3=r6c3} - 4b3{r3c8=r1c9} - 6r1{r1c9=r1c1} - 1r1{r1c1=r1c3} - 7c3{r1c3=.}
g-Braid[9]: => r2c8<>3
3r2c8 - 3b6{r4c8=r6c9} - 3c3{r6c3=r3c3} - 3r8{r8c9=r8c6} - 2r8{r8c6=r8c9} - 2b6{r5c9=r5c7} - 2c3{r5c3=r6c3} - 7c3{r6c3=r1c3} - 7b2{r1c4=r23c4} - 7r8{r8c4=.}
g-Braid[7]: => r3c3<>2
2r3c3 - 2b2{r3c4=r2c4} - 3c3{r3c3=r6c3} - 7c3{r6c3=r1c3} - 7b2{r1c4=r3c4} - 5b2{r3c4=r1c456} - r1c7{n5=n8} - 8b2{r1c4=.}
Whip[1]: => r4c2<>2
2r4c2 - 2c3{r5c3=.}
Whip[1]: => r5c2<>2
2r5c2 - 2c3{r5c3=.}
Whip[1]: => r5c5<>2
2r5c5 - 2r4{r4c5=.}
Whip[1]: => r6c2<>2
2r6c2 - 2c3{r5c3=.}
Whip[1]: => r6c5<>2
2r6c5 - 2r4{r4c5=.}
Whip[1]: => r6c6<>2
2r6c6 - 2r4{r4c5=.}
Whip[4]: => r3c9<>3
3r3c9 - 3c7{r2c7=r9c7} - 2c7{r9c7=r5c7} - 2b4{r5c3=r6c3} - 3c3{r6c3=.}
Braid[6]: => r4c5<>4
4r4c5 - 2b5{r4c5=r4c6} - 4b8{r7c5=r9c4} - 6b8{r9c4=r8c4} - 1c4{r8c4=r6c4} - 8b5{r6c4=r6c6} - 9c6{r6c6=.}
g-Braid[7]: => r6c3<>1
1r6c3 - 2r6{r6c3=r6c9} - 2r8{r8c9=r8c6} - 3b6{r6c9=r46c8} - 3r8{r8c8=r8c9} - 7r8{r8c9=r8c4} - 1c4{r8c4=r9c4} - 6c4{r9c4=.}
Braid[7]: => r6c3<>4
4r6c3 - 3c3{r6c3=r3c3} - 4r7{r7c3=r7c5} - 4r5{r5c5=r5c9} - 4r1{r1c9=r1c1} - 6r1{r1c1=r1c9} - 1r1{r1c9=r1c3} - 7c3{r1c3=.}
g-Braid[8]: => r6c3<>9
9r6c3 - 2r6{r6c3=r6c9} - 2r8{r8c9=r8c6} - 3b6{r6c9=r46c8} - 3r8{r8c8=r8c9} - 7r8{r8c9=r8c4} - 7b2{r1c4=r1c56} - 7c3{r1c3=r3c3} - 3c3{r3c3=.}
g-Whip[6]: => r8c6<>3
3r8c6 - 2r8{r8c6=r8c9} - 2r6{r6c9=r6c3} - 3c3{r6c3=r3c3} - 7c3{r3c3=r1c3} - 7b2{r1c4=r23c4} - 7r8{r8c4=.}
Whip[1]: => r9c7<>3
3r9c7 - 3r8{r8c8=.}
Whip[1]: => r2c9<>3
3r2c9 - 3c7{r2c7=.}
Whip[1]: => r9c8<>3
3r9c8 - 3r8{r8c8=.}
Whip[1]: => r9c9<>3
3r9c9 - 3r8{r8c8=.}
g-Whip[6]: => r3c3<>8
8r3c3 - 3c3{r3c3=r6c3} - 3c9{r6c9=r8c9} - 2r8{r8c9=r8c6} - 7r8{r8c6=r8c4} - 7b2{r1c4=r1c56} - 7c3{r1c3=.}
Whip[6]: => r6c9<>4
4r6c9 - 2r6{r6c9=r6c3} - 3c3{r6c3=r3c3} - 7c3{r3c3=r1c3} - 4r1{r1c3=r1c1} - 1r1{r1c1=r1c9} - 6r1{r1c9=.}
g-Braid[7]: => r6c9<>5
5r6c9 - 2r6{r6c9=r6c3} - 3c9{r6c9=r8c9} - 2r8{r8c9=r8c6} - 7r8{r8c6=r8c4} - 7b2{r1c4=r1c56} - 7c3{r1c3=r3c3} - 3c3{r3c3=.}
g-Braid[7]: => r6c9<>9
9r6c9 - 2r6{r6c9=r6c3} - 3c9{r6c9=r8c9} - 2r8{r8c9=r8c6} - 7r8{r8c6=r8c4} - 7b2{r1c4=r1c56} - 7c3{r1c3=r3c3} - 3c3{r3c3=.}
g-Braid[7]: => r8c9<>1
1r8c9 - 2r8{r8c9=r8c6} - 3c9{r8c9=r6c9} - 2r6{r6c9=r6c3} - 3c3{r6c3=r3c3} - 7c3{r3c3=r1c3} - 7b2{r1c4=r23c4} - 7r8{r8c4=.}
g-Braid[7]: => r8c9<>5
5r8c9 - 2r8{r8c9=r8c6} - 3c9{r8c9=r6c9} - 2r6{r6c9=r6c3} - 3c3{r6c3=r3c3} - 7c3{r3c3=r1c3} - 7b2{r1c4=r23c4} - 7r8{r8c4=.}
g-Braid[7]: => r8c9<>9
9r8c9 - 2r8{r8c9=r8c6} - 3c9{r8c9=r6c9} - 2r6{r6c9=r6c3} - 3c3{r6c3=r3c3} - 7c3{r3c3=r1c3} - 7b2{r1c4=r23c4} - 7r8{r8c4=.}
Whip[8]: => r4c1<>9
9r4c1 - 3r4{r4c1=r4c8} - 3b9{r8c8=r8c9} - 2r8{r8c9=r8c6} - 7r8{r8c6=r8c4} - 6b8{r8c4=r9c4} - 1c4{r9c4=r6c4} - 8b5{r6c4=r6c6} - 9c6{r6c6=.}
Braid[9]: => r6c1<>3
3r6c1 - r6c9{n3=n2} - 3b6{r6c8=r4c8} - r6c3{n2=n7} - 2r8{r8c9=r8c6} - 9r4{r4c8=r4c6} - 2b5{r4c6=r4c5} - 7b5{r4c5=r4c4} - 7r8{r8c4=r8c9} - 3r8{r8c9=.}
g-Braid[10]: => r6c8<>3
3r6c8 - r6c9{n3=n2} - 3b9{r8c8=r8c9} - r6c3{n2=n7} - 2b9{r8c9=r9c7} - 7b9{r8c9=r7c79} - r7c6{n7=n5} - r9c6{n5=n3} - 3b2{r1c6=r1c5} - 7c5{r1c5=r4c5} - 2c5{r4c5=.}
Whip[2]: => r6c3<>7
7r6c3 - 2r6{r6c3=r6c9} - 3r6{r6c9=.}
Whip[1]: => r2c2<>7
7r2c2 - 7c3{r1c3=.}
Whip[1]: => r3c2<>7
7r3c2 - 7c3{r1c3=.}
g-Braid[5]: => r3c4<>7
7r3c4 - 2b2{r3c4=r2c4} - 7b1{r3c3=r1c3} - 5b2{r3c4=r1c456} - r1c7{n5=n8} - 8b2{r1c4=.}
g-Whip[5]: => r1c3<>7
7r1c3 - 7b2{r1c4=r2c4} - 2b2{r2c4=r3c4} - 5b2{r3c4=r1c456} - r1c7{n5=n8} - 8b2{r1c4=.}
stte


[denis_berthier]

.
We already know there are bugs in Mauricio's solver.
.

[yzfwsf]

3. What is the longest whip rating of the first step of the solution of a puzzle (answer is >=32, the first whip of the following puzzle has length 32, 000001002010030040005600000007100004030008000100040900000002007080000030900800600

What is the longest Braid rating of the first step of the solution of a puzzle (answer is >=30, the first Braid of the following puzzle has length 30

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.....1..2....3..4...56..7....6...5...1......37..8...9...9..5.8..2..4....3..7..9..

[denis_berthier]

What is the longest Braid rating of the first step of the solution of a puzzle (answer is >=30, the first Braid of the following puzzle has length 30

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.....1..2....3..4...56..7....6...5...1......37..8...9...9..5.8..2..4....3..7..9..

... and the solution is in B30.

Great example! Until now, we knew only one puzzle in B30, by Mauricio (like the very few currently known highest W, B, gW, gB ratings):
.....1..2....3..4...15..6....71..8...2..9...71....4.5...86......4...7.9.3...5....

Did you find yours by vicinity search from some of Mauricio's puzzles ?

[yzfwsf]

Did you find yours by vicinity search from some of Mauricio's puzzles ?

No, this puzzle is taken from the pattern game 0383 and is posted by 1to9only(#13). I have checked all the puzzles for ER9.4 to ER9.6 in the patterns game

[yzfwsf]

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000009007004030010080100000001000002030080040700000500000005600090040030200900000 # 136    9.9/9.9/9.3 - BryanL  Patterns Game 0131

This puzzle is the one with the highest gB rating I have found so far. gB rating=g-Braid[29]

[denis_berthier]

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000009007004030010080100000001000002030080040700000500000005600090040030200900000 ER9.9/9.9/9.3

This puzzle is the one with the highest gB rating I have found so far. gB rating=g-Braid[29]

Great.
It should be mentioned that the puzzle is not in T&E(1), so that its B rating is infinite.

Also, when you post a puzzle, could you systematically mention its origin?

[yzfwsf]

It should be mentioned that the puzzle is not in T&E(1), so that its B rating is infinite.

1. What is the lowest braid rating of a puzzle not solvable by pure braids (answer is 3, 001002003000010040200400500006007008050000020900300400008001005090060000100900700

How about Mauricio's first puzzle?

[denis_berthier]

1. What is the lowest braid rating of a puzzle not solvable by pure braids (answer is 3, 001002003000010040200400500006007008050000020900300400008001005090060000100900700

The B rating of a puzzle not solvable by braids is infinite. The question makes no sense.

Again: who's the author of the gB29 puzzle: 000009007004030010080100000001000002030080040700000500000005600090040030200900000 ER9.9/9.9/9.3

[yzfwsf]

The B rating of a puzzle not solvable by braids is infinite. The question makes no sense.

Mauricio's puzzle is also in T&E(Single,2), but gB-Rating=2

Again: who's the author of the gB29 puzzle: 000009007004030010080100000001000002030080040700000500000005600090040030200900000 ER9.9/9.9/9.3

Don't you look at the original post? I have added notes on the author and source.

[denis_berthier]

The B rating of a puzzle not solvable by braids is infinite. The question makes no sense.

Mauricio's puzzle is also in T&E(Single,2), but gB-Rating=2

If you speak of the gB rating, it makes sense.
But this example (B infinite, gB = 2) is not new. It was already in [CRT] in 2011.

Again: who's the author of the gB29 puzzle: 000009007004030010080100000001000002030080040700000500000005600090040030200900000 ER9.9/9.9/9.3

Don't you look at the original post? I have added notes on the author and source.

[/quote]
Ah, no, I hadn't seen the addition. Thanks.

[yzfwsf]

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005000000070006080200040009009100002020080040300002600100020004030800070000000500 9.7/9.7/9.7 t&e1 - JPF game 0441

After some steps, we get this RS.

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,---------------------,-------------------,--------------------,
| 4689   14689  5     | 2379  1379  13789 | 12347  1236   1367 |
| 49     7      134   | 239   139   6     | 1234   8      5    |
| 2      168    1368  | 357   4     13578 | 137    136    9    |
:---------------------+-------------------+--------------------:
| 45678  468    9     | 1     3567  3457  | 378    35     2    |
| 567    2      167   | 3679  8     3579  | 139    4      137  |
| 3      148    147   | 4579  579   2     | 6      159    78   |
:---------------------+-------------------+--------------------:
| 1      5      678   | 3679  2     379   | 389    369    4    |
| 469    3      246   | 8     1569  1459  | 129    7      16   |
| 678    689    24678 | 346   1367  13479 | 5      12369  1368 |
'---------------------'-------------------'--------------------'

Finding a valid g-Braid for r9c2<>8 has become an impossible task. Firstly, BFS may encounter the dilemma of insufficient memory, so I changed the algorithm to controlled DFS, which now leads to a situation of excessively long running time.

[denis_berthier]

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005000000070006080200040009009100002020080040300002600100020004030800070000000500 9.7/9.7/9.7 t&e1 - JPF game 0441

Firstly, BFS may encounter the dilemma of insufficient memory, so I changed the algorithm to controlled DFS, which now leads to a situation of excessively long running time.

SudoRules finds a solution with DFS or T&E(W1, 1), with no problem of memory or time.