- Code: Select all
+-------+-------+-------+
! . . . ! 1 . . ! . 8 . !
! . . 3 ! . . . ! 9 . . !
! . 6 2 ! . . 3 ! . . . !
+-------+-------+-------+
! . 1 . ! . 2 . ! . . . !
! 2 . . ! 8 7 . ! . . 3 !
! . . . ! . 4 . ! . 1 . !
+-------+-------+-------+
! . . . ! 9 . . ! 8 4 . !
! . . 6 ! . . . ! 1 . . !
! . 4 . ! . . 5 ! . . . !
+-------+-------+-------+
...1...8...3...9...62..3....1..2....2..87...3....4..1....9..84...6...1...4...5... # 1903 FNBTHWXY C22.m
SER = 8.2
Lightning 8.2
2 posts
• Page 1 of 1
Lightning 8.2
by denis_berthier » Thu Apr 15, 2021 4:30 am
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- denis_berthier
- 2010 Supporter
- Posts: 4238
- Joined: 19 June 2007
- Location: Paris
Re: Lightning 8.2
by denis_berthier » Sat Apr 17, 2021 8:44 am
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This puzzle doesn't seem to have any reasonable 1-step or 2-step solution.
But it has a relatively easy solution in Z4, i.e. using only very short reversible chains. It's a good example for anyone wanting to learn z-chains.
Resolution state after Singles and whips[1]:
naked-pairs-in-a-column: c6{r4 r6}{n6 n9} ==> r7c6 ≠ 6, r2c6 ≠ 6, r1c6 ≠ 6
whip[1]: c6n6{r6 .} ==> r4c4 ≠ 6, r6c4 ≠ 6
hidden-pairs-in-a-row: r3{n8 n9}{c1 c5} ==> r3c5 ≠ 5, r3c1 ≠ 7, r3c1 ≠ 5, r3c1 ≠ 4, r3c1 ≠ 1
singles ==> r2c1 = 1, r3c9 = 1
whip[1]: r3n5{c8 .} ==> r1c9 ≠ 5, r2c8 ≠ 5, r2c9 ≠ 5
whip[1]: b1n4{r1c3 .} ==> r1c6 ≠ 4, r1c9 ≠ 4
naked-pairs-in-a-column: c6{r1 r7}{n2 n7} ==> r8c6 ≠ 7, r8c6 ≠ 2, r2c6 ≠ 7, r2c6 ≠ 2
x-wing-in-rows: n6{r1 r7}{c5 c9} ==> r9c9 ≠ 6, r9c5 ≠ 6, r2c9 ≠ 6, r2c5 ≠ 6
finned-x-wing-in-rows: n8{r3 r9}{c5 c1} ==> r8c1 ≠ 8
biv-chain[3]: c1n6{r6 r4} - r4n3{c1 c4} - b5n5{r4c4 r6c4} ==> r6c1 ≠ 5
biv-chain[3]: c4n6{r9 r2} - b2n2{r2c4 r1c6} - c6n7{r1 r7} ==> r9c4 ≠ 7
biv-chain[3]: r7c6{n7 n2} - r9c4{n2 n6} - r7n6{c5 c9} ==> r7c9 ≠ 7
z-chain[3]: r9c4{n2 n6} - r2n6{c4 c8} - c8n2{r2 .} ==> r9c9 ≠ 2, r9c7 ≠ 2
hidden-single-in-a-column ==> r6c7 = 2
biv-chain[4]: r3n8{c1 c5} - r2c6{n8 n4} - c9n4{r2 r4} - b6n8{r4c9 r6c9} ==> r6c1 ≠ 8
z-chain[4]: c8n3{r8 r9} - r9n2{c8 c4} - b8n6{r9c4 r7c5} - r7n3{c5 .} ==> r8c2 ≠ 3, r8c1 ≠ 3
z-chain[4]: r2n6{c4 c8} - r2n2{c8 c9} - b3n4{r2c9 r3c7} - r3c4{n4 .} ==> r2c4 ≠ 7
biv-chain[4]: b2n7{r3c4 r1c6} - b2n2{r1c6 r2c4} - r9c4{n2 n6} - r9c7{n6 n7} ==> r3c7 ≠ 7
biv-chain[4]: b2n7{r1c6 r3c4} - r3n4{c4 c7} - c9n4{r2 r4} - c1n4{r4 r1} ==> r1c1 ≠ 7
z-chain[2]: b1n7{r2c2 r1c3} - c6n7{r1 .} ==> r7c2 ≠ 7
z-chain[4]: r9n1{c5 c3} - r9n8{c3 c1} - r3n8{c1 c5} - r8c5{n8 .} ==> r9c5 ≠ 3
biv-chain[3]: r7n6{c9 c5} - c5n3{r7 r8} - b9n3{r8c8 r9c8} ==> r9c8 ≠ 6
biv-chain[4]: r9c7{n7 n6} - r7n6{c9 c5} - c5n3{r7 r8} - b9n3{r8c8 r9c8} ==> r9c8 ≠ 7
biv-chain[4]: r9n2{c8 c4} - b8n6{r9c4 r7c5} - c5n3{r7 r8} - b9n3{r8c8 r9c8} ==> r9c8 ≠ 9
biv-chain[4]: b8n3{r7c5 r8c5} - b9n3{r8c8 r9c8} - r9n2{c8 c4} - b8n6{r9c4 r7c5} ==> r7c5 ≠ 1
singles ==> r9c5 = 1, r7c3 = 1
whip[1]: r9n8{c3 .} ==> r8c2 ≠ 8
biv-chain[4]: r8c5{n3 n8} - r3n8{c5 c1} - c2n8{r2 r6} - c2n3{r6 r7} ==> r7c5 ≠ 3
stte
This puzzle doesn't seem to have any reasonable 1-step or 2-step solution.
But it has a relatively easy solution in Z4, i.e. using only very short reversible chains. It's a good example for anyone wanting to learn z-chains.
Resolution state after Singles and whips[1]:
- Code: Select all
+-------------------------+-------------------------+-------------------------+
! 4579 579 4579 ! 1 569 2467 ! 3 8 24567 !
! 14578 578 3 ! 2467 568 24678 ! 9 2567 124567 !
! 145789 6 2 ! 47 589 3 ! 457 57 1457 !
+-------------------------+-------------------------+-------------------------+
! 3456789 1 45789 ! 356 2 69 ! 457 579 45789 !
! 2 59 459 ! 8 7 1 ! 456 569 3 !
! 356789 35789 5789 ! 356 4 69 ! 257 1 25789 !
+-------------------------+-------------------------+-------------------------+
! 357 2357 157 ! 9 136 267 ! 8 4 2567 !
! 35789 235789 6 ! 247 38 2478 ! 1 23579 2579 !
! 3789 4 1789 ! 267 1368 5 ! 267 23679 2679 !
+-------------------------+-------------------------+-------------------------+
naked-pairs-in-a-column: c6{r4 r6}{n6 n9} ==> r7c6 ≠ 6, r2c6 ≠ 6, r1c6 ≠ 6
whip[1]: c6n6{r6 .} ==> r4c4 ≠ 6, r6c4 ≠ 6
hidden-pairs-in-a-row: r3{n8 n9}{c1 c5} ==> r3c5 ≠ 5, r3c1 ≠ 7, r3c1 ≠ 5, r3c1 ≠ 4, r3c1 ≠ 1
singles ==> r2c1 = 1, r3c9 = 1
whip[1]: r3n5{c8 .} ==> r1c9 ≠ 5, r2c8 ≠ 5, r2c9 ≠ 5
whip[1]: b1n4{r1c3 .} ==> r1c6 ≠ 4, r1c9 ≠ 4
naked-pairs-in-a-column: c6{r1 r7}{n2 n7} ==> r8c6 ≠ 7, r8c6 ≠ 2, r2c6 ≠ 7, r2c6 ≠ 2
x-wing-in-rows: n6{r1 r7}{c5 c9} ==> r9c9 ≠ 6, r9c5 ≠ 6, r2c9 ≠ 6, r2c5 ≠ 6
finned-x-wing-in-rows: n8{r3 r9}{c5 c1} ==> r8c1 ≠ 8
biv-chain[3]: c1n6{r6 r4} - r4n3{c1 c4} - b5n5{r4c4 r6c4} ==> r6c1 ≠ 5
biv-chain[3]: c4n6{r9 r2} - b2n2{r2c4 r1c6} - c6n7{r1 r7} ==> r9c4 ≠ 7
biv-chain[3]: r7c6{n7 n2} - r9c4{n2 n6} - r7n6{c5 c9} ==> r7c9 ≠ 7
z-chain[3]: r9c4{n2 n6} - r2n6{c4 c8} - c8n2{r2 .} ==> r9c9 ≠ 2, r9c7 ≠ 2
hidden-single-in-a-column ==> r6c7 = 2
biv-chain[4]: r3n8{c1 c5} - r2c6{n8 n4} - c9n4{r2 r4} - b6n8{r4c9 r6c9} ==> r6c1 ≠ 8
z-chain[4]: c8n3{r8 r9} - r9n2{c8 c4} - b8n6{r9c4 r7c5} - r7n3{c5 .} ==> r8c2 ≠ 3, r8c1 ≠ 3
z-chain[4]: r2n6{c4 c8} - r2n2{c8 c9} - b3n4{r2c9 r3c7} - r3c4{n4 .} ==> r2c4 ≠ 7
biv-chain[4]: b2n7{r3c4 r1c6} - b2n2{r1c6 r2c4} - r9c4{n2 n6} - r9c7{n6 n7} ==> r3c7 ≠ 7
biv-chain[4]: b2n7{r1c6 r3c4} - r3n4{c4 c7} - c9n4{r2 r4} - c1n4{r4 r1} ==> r1c1 ≠ 7
z-chain[2]: b1n7{r2c2 r1c3} - c6n7{r1 .} ==> r7c2 ≠ 7
z-chain[4]: r9n1{c5 c3} - r9n8{c3 c1} - r3n8{c1 c5} - r8c5{n8 .} ==> r9c5 ≠ 3
biv-chain[3]: r7n6{c9 c5} - c5n3{r7 r8} - b9n3{r8c8 r9c8} ==> r9c8 ≠ 6
biv-chain[4]: r9c7{n7 n6} - r7n6{c9 c5} - c5n3{r7 r8} - b9n3{r8c8 r9c8} ==> r9c8 ≠ 7
biv-chain[4]: r9n2{c8 c4} - b8n6{r9c4 r7c5} - c5n3{r7 r8} - b9n3{r8c8 r9c8} ==> r9c8 ≠ 9
biv-chain[4]: b8n3{r7c5 r8c5} - b9n3{r8c8 r9c8} - r9n2{c8 c4} - b8n6{r9c4 r7c5} ==> r7c5 ≠ 1
singles ==> r9c5 = 1, r7c3 = 1
whip[1]: r9n8{c3 .} ==> r8c2 ≠ 8
biv-chain[4]: r8c5{n3 n8} - r3n8{c5 c1} - c2n8{r2 r6} - c2n3{r6 r7} ==> r7c5 ≠ 3
stte
- denis_berthier
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- Joined: 19 June 2007
- Location: Paris
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