I'm still not too familiar with the rating but I would name it a 1.25. I wonder what you think about it.
Walkthrough is coming...
Cheers,
Nasenbaer
Assassin 81
Assassin 81
A nice puzzle with an easy start which made me overconfident so I didn't take full notes. Now I have to take the scraps and put them in a proper walkthrough. Oh well.
I'm still not too familiar with the rating but I would name it a 1.25. I wonder what you think about it.
Walkthrough is coming...
Cheers,
Nasenbaer
I'm still not too familiar with the rating but I would name it a 1.25. I wonder what you think about it.
Walkthrough is coming...
Cheers,
Nasenbaer
... walkthrough arrived.
I missed a major move in r2c159 on my first go and found it late in the second one (step 29). If I had spotted it earlier the puzzle might have broken faster. But now I'm too lazy to rewrite the walkthrough.
I used the term CP for Cage Placement, that means looking at all possible combinations and how they could be placed in the cage.
Walkthrough Assassin 81
Preliminaries:
0a. n3: 4(2) = {13} -> 1,3 locked for n3 and c9
0b. n9: 10(2) = {28|46}
0c. n1: 12(4) = 12{36|45} -> 1,2 locked for n1
0d. n3: 28(4) = 89{47|56} -> 8,9 locked for n3
0e. n1: 12(2) = {39|48|57}
0f. 11(3) in n4 and n6: no 9
0g. n47: 22(3) = 9{58|67} -> 9 locked for 22(3) -> no 9 in r4c2
0h. n7: 14(2) = {59|68}
0i. n4578: 14(4): no 9
0j. n5: 8(2) = {17|26|35}
0k. n8: 7(2) = {16|25|34}
1. 45 on r5: r5c456 = h23(3) = {689}
1a. -> r5c6 = 6 -> r4c6 = 2
1b. 8,9 locked in r5c45 for n5 and r5
2. 45 on r1234: r4c4 = 7
3. 45 on n5: r4c5 + r6c4 = h7(2) = {34} -> 3,4 locked for n5
3a. -> r6c56 = {15} -> 1,5 locked for n5 and r6
4. n4: 11(3) = {137|245}
5. n6: 11(3) = {137|245}
6. 45 on c1234: r5c4 = r1c5 = {89}
6a. r15c5 = {89} -> 8,9 locked for c5
7. 45 on c6789: r9c5 = r5c6 + 1 -> r9c5 = {26}
8. c5: 7(2) : {34} blocked by r4c5
8a. r6789c5 = {1256} -> 1,2,5,6 locked for c5, 2,6 locked for n8
8b. 14(3) = {347} -> 7 locked for n2
9. n6: CP in 11(3): no 7 in r5c78
10. 45 on n1: r1c3 + r3c23 = h21(3) = {489|579|678} -> no 3
11. 45 on n3: r1c7 + r3c78 = h13(3) = 2{47|56} -> 2 locked for h13(3) and n3
12. 45 on n7: r7c23 + r9c3 = h12(3) = {129|138|147|237|246|345} ({156} blocked by 14(2))
12a. CP for h12(3): r79c3 = {1234}
13. 45 on n9: r7c78 + r9c7 = h13(3) = {139|157|238|346} (other combinations blocked by 10(2))
14. n47: CP for 22(3): no 8 in r7c2
14a. -> n9: {138} removed from h12(3)
15. c1: 8 locked in 12(2) and 14(2) for c1 (14(2) = {68} or 14(2) = {59} -> 12(2) = {48})
15a. 9 locked in 12(2), 14(2) and r6c1 for c1
16. n14: 14(3) = {149|158|167|356} ({347} blocked by r4c5)
16a. CP: {149} blocked by 11(3) -> no 4,9 in 14(3)
16b. CP: 11(3) blocks some placements of remaining combinations -> r3c2 = {57}, r4c1 = {136}, r4c2 =
{1368}
16c. -> 14(3) has 1 or 3 in r4c12 -> n4: 11(2) = {245} -> 2,4,5 locked for n4 and r5
16d. -> n6: 11(3) = {137} -> 1,3,7 locked for n6 and r5 -> r5c9 = 7
17. c1: 12(2): {57} blocked by r3c2
17a. -> {89} locked in 12(2) and 14(2) for c1 -> no 9 in r6c1
18. n47: 22(3) = {679} -> 9 locked in r67c2 for c2 -> no 6 in r4c2
18a. n7: {345} removed from h12(3)
18b. n14: 14(3): no 3 in r4c1
19. n1: h21(3) = 7{59|68} -> no 4
20. 45 on c12: r258c3 = h14(3) = {149|158|239|248|257|347|356}
20a. CP: no 1,2,4,5 in r8c3
21. 45 on r89: r8c159 = h16(3) = {169|259|268}
21a. -> no 4 in r8c9 -> no 6 in r7c9
21b. CP for h16(3): no 5 in r8c1 -> no 9 in r7c1
22. 45 on r12: r2c159 = h14(3) = 4{19|37} -> 4 locked in r2c15 for r2
22a. CP: no 3 in r2c15
22b. -> no 4,9 in r3c1
23. n36: 17(3) = {269|458|467}
23a. CP: no 6 in r3c8
23b. {68} locked in r4c1289 for r4
24. n124: 18(3) = {189|279|369|378|459}
24a. CP: no 5 in r3c4
25. r236: 16(3) = {169|259|349|457} ({358} not possible) -> no 8 in r3c6
25a. CP: no 5 in r3c7
26. 45 on c89: r258c7 = h17(3) = {179|359|368}
26a. CP: no 1,2,3,4 in r8c7
27. n69: 15(3) = {168|249|258|267|348|456}
27a. CP: no 9 in r6c8 ({24} in r6c9 r7c8 blocked by 10(2) at r7c9)
27b. CP: no 6,8 in r7c8
28. n23: 14(3) = {149|158|239|248|356} ({347} blocked by c2:h14(3)) -> no 7 in r1c7
This move should have come a lot earlier, I didn't see it until now
29. c2: h14(3): [941] not possible, would place 3 in r3c1 and r3c9 -> conflict
29a. -> r2c159 = [473], r3c19 = [81]
30. n1: h21(3) = {579} -> 9 locked in r13c3 for n1 and c3, 5,7 locked for n1
30a. 3 locked in r1c12 for n1 and r1
31. n124: 18(3): r4c3 = 3, r3c34 = [96]
31a. r34c5 = [34], r6c4 = 3, r78c1 = [59], r5c1 = 2, r6c2 = 9
32. n8: 7(2): no 2 in r8c5
32a. r8: h16(3) = 9[16|52] -> no 1 in r7c5, no 2 in r7c9
33. n3: 2 locked in r3c78 for n3 and r3
34. n236: 16(3) = 5{29|47} -> CP: no 4 in r3c7
34a. n3: h13(3): CP: no 5 in r1c7, no 4 in r3c8
from here on it's simple cleaning up
34b. n36: 17(3): CP: r3c8 = 2, r4c89 = {69} -> 6,9 locked for r4 and n6
34c. r4c127 = [185], r3c267 = [547], r16c3 = [76], r5c23 = [45], r6c1 = 7, r7c2 = 6, r8c379 = [862]
34d. r6789c5 = [1256], r6c6 = 5, r19c1 = [63], r67c9 = [48], r4c89 = [96], r1c27 = [34]
34e. r6c78 = [28], r1257c8 = [5613], ...
[/size]
Coments are appreciated.
Edit: Corrections in blue, thanks to Andrew.
Cheers,
Nasenbaer
I missed a major move in r2c159 on my first go and found it late in the second one (step 29). If I had spotted it earlier the puzzle might have broken faster. But now I'm too lazy to rewrite the walkthrough.
I used the term CP for Cage Placement, that means looking at all possible combinations and how they could be placed in the cage.
Walkthrough Assassin 81
Preliminaries:
0a. n3: 4(2) = {13} -> 1,3 locked for n3 and c9
0b. n9: 10(2) = {28|46}
0c. n1: 12(4) = 12{36|45} -> 1,2 locked for n1
0d. n3: 28(4) = 89{47|56} -> 8,9 locked for n3
0e. n1: 12(2) = {39|48|57}
0f. 11(3) in n4 and n6: no 9
0g. n47: 22(3) = 9{58|67} -> 9 locked for 22(3) -> no 9 in r4c2
0h. n7: 14(2) = {59|68}
0i. n4578: 14(4): no 9
0j. n5: 8(2) = {17|26|35}
0k. n8: 7(2) = {16|25|34}
1. 45 on r5: r5c456 = h23(3) = {689}
1a. -> r5c6 = 6 -> r4c6 = 2
1b. 8,9 locked in r5c45 for n5 and r5
2. 45 on r1234: r4c4 = 7
3. 45 on n5: r4c5 + r6c4 = h7(2) = {34} -> 3,4 locked for n5
3a. -> r6c56 = {15} -> 1,5 locked for n5 and r6
4. n4: 11(3) = {137|245}
5. n6: 11(3) = {137|245}
6. 45 on c1234: r5c4 = r1c5 = {89}
6a. r15c5 = {89} -> 8,9 locked for c5
7. 45 on c6789: r9c5 = r5c6 + 1 -> r9c5 = {26}
8. c5: 7(2) : {34} blocked by r4c5
8a. r6789c5 = {1256} -> 1,2,5,6 locked for c5, 2,6 locked for n8
8b. 14(3) = {347} -> 7 locked for n2
9. n6: CP in 11(3): no 7 in r5c78
10. 45 on n1: r1c3 + r3c23 = h21(3) = {489|579|678} -> no 3
11. 45 on n3: r1c7 + r3c78 = h13(3) = 2{47|56} -> 2 locked for h13(3) and n3
12. 45 on n7: r7c23 + r9c3 = h12(3) = {129|138|147|237|246|345} ({156} blocked by 14(2))
12a. CP for h12(3): r79c3 = {1234}
13. 45 on n9: r7c78 + r9c7 = h13(3) = {139|157|238|346} (other combinations blocked by 10(2))
14. n47: CP for 22(3): no 8 in r7c2
14a. -> n9: {138} removed from h12(3)
15. c1: 8 locked in 12(2) and 14(2) for c1 (14(2) = {68} or 14(2) = {59} -> 12(2) = {48})
15a. 9 locked in 12(2), 14(2) and r6c1 for c1
16. n14: 14(3) = {149|158|167|356} ({347} blocked by r4c5)
16a. CP: {149} blocked by 11(3) -> no 4,9 in 14(3)
16b. CP: 11(3) blocks some placements of remaining combinations -> r3c2 = {57}, r4c1 = {136}, r4c2 =
{1368}
16c. -> 14(3) has 1 or 3 in r4c12 -> n4: 11(2) = {245} -> 2,4,5 locked for n4 and r5
16d. -> n6: 11(3) = {137} -> 1,3,7 locked for n6 and r5 -> r5c9 = 7
17. c1: 12(2): {57} blocked by r3c2
17a. -> {89} locked in 12(2) and 14(2) for c1 -> no 9 in r6c1
18. n47: 22(3) = {679} -> 9 locked in r67c2 for c2 -> no 6 in r4c2
18a. n7: {345} removed from h12(3)
18b. n14: 14(3): no 3 in r4c1
19. n1: h21(3) = 7{59|68} -> no 4
20. 45 on c12: r258c3 = h14(3) = {149|158|239|248|257|347|356}
20a. CP: no 1,2,4,5 in r8c3
21. 45 on r89: r8c159 = h16(3) = {169|259|268}
21a. -> no 4 in r8c9 -> no 6 in r7c9
21b. CP for h16(3): no 5 in r8c1 -> no 9 in r7c1
22. 45 on r12: r2c159 = h14(3) = 4{19|37} -> 4 locked in r2c15 for r2
22a. CP: no 3 in r2c15
22b. -> no 4,9 in r3c1
23. n36: 17(3) = {269|458|467}
23a. CP: no 6 in r3c8
23b. {68} locked in r4c1289 for r4
24. n124: 18(3) = {189|279|369|378|459}
24a. CP: no 5 in r3c4
25. r236: 16(3) = {169|259|349|457} ({358} not possible) -> no 8 in r3c6
25a. CP: no 5 in r3c7
26. 45 on c89: r258c7 = h17(3) = {179|359|368}
26a. CP: no 1,2,3,4 in r8c7
27. n69: 15(3) = {168|249|258|267|348|456}
27a. CP: no 9 in r6c8 ({24} in r6c9 r7c8 blocked by 10(2) at r7c9)
27b. CP: no 6,8 in r7c8
28. n23: 14(3) = {149|158|239|248|356} ({347} blocked by c2:h14(3)) -> no 7 in r1c7
This move should have come a lot earlier, I didn't see it until now
29. c2: h14(3): [941] not possible, would place 3 in r3c1 and r3c9 -> conflict
29a. -> r2c159 = [473], r3c19 = [81]
30. n1: h21(3) = {579} -> 9 locked in r13c3 for n1 and c3, 5,7 locked for n1
30a. 3 locked in r1c12 for n1 and r1
31. n124: 18(3): r4c3 = 3, r3c34 = [96]
31a. r34c5 = [34], r6c4 = 3, r78c1 = [59], r5c1 = 2, r6c2 = 9
32. n8: 7(2): no 2 in r8c5
32a. r8: h16(3) = 9[16|52] -> no 1 in r7c5, no 2 in r7c9
33. n3: 2 locked in r3c78 for n3 and r3
34. n236: 16(3) = 5{29|47} -> CP: no 4 in r3c7
34a. n3: h13(3): CP: no 5 in r1c7, no 4 in r3c8
from here on it's simple cleaning up
34b. n36: 17(3): CP: r3c8 = 2, r4c89 = {69} -> 6,9 locked for r4 and n6
34c. r4c127 = [185], r3c267 = [547], r16c3 = [76], r5c23 = [45], r6c1 = 7, r7c2 = 6, r8c379 = [862]
34d. r6789c5 = [1256], r6c6 = 5, r19c1 = [63], r67c9 = [48], r4c89 = [96], r1c27 = [34]
34e. r6c78 = [28], r1257c8 = [5613], ...
[/size]
Coments are appreciated.
Edit: Corrections in blue, thanks to Andrew.
Cheers,
Nasenbaer
Last edited by Nasenbaer on Sat Dec 22, 2007 2:54 pm, edited 2 times in total.
This was an easy but nonetheless fun assassin. I was quite suprised that I could make some placements right from the start.
A81 Walkthrough:
1. N5+C5
a) Innies R5 = 23(3) = {689} locked for R5+N5; R5C6 = 6
b) 8(2) = [26] -> R4C6 = 2
c) 30(5) = {15789} locked for N5
d) 7(2) <> 3,4 because R4C5 = (34)
e) 14(3) <> 5,6 because R4C5 = (34) and {356} blocked by Killer pair (56) of 7(2)
2. C6789
a) 4(2) = {13} locked for C9+N3
b) 28(4) = 89{47/56}; (89) locked for N3
c) 10(2) <> 7,9
d) Innies+Outies: 1 = R9C5 - R6C6 -> R9C5 = (268)
3. R1234
a) Innies R1234 = 7 = R4C4
b) Innies R12 = 14(3): R2C15 <> 1,3 because R2C9 = (13)
c) Innies N1 = 21(3) <> 1,2,3
d) 12(2): R3C1 <> 9
4. C45
a) 7 locked in R123C5 for N2
b) Innies+Outies C1234: R1C5 = R5C4 = (89)
c) Naked pair (89) locked for R15C5 for C5
d) 14(3) = {347}
e) 2,6 locked in R123C4 for C4
5. N7+R6
a) 30(5) = {15789} -> 1,5 locked for R6
b) Innies N7 = 12(3): R79C3 <> 7,8,9 because R7C2 >= 5
c) Innies N7 = 12(3): R79C3 <> 5,6 because {156} blocked by Killer pair (56) of 14(2)
6. ! R12
a) Innies R12 = 14(3) = 4{19/37}, 4 locked for R2
b) 12(2): R3C1 <> 4,7
c) ! Innies+Outies R12: 2 = R3C19 - R2C5; R2C5 = (47)
-> R3C19 = 6/9(2) = 1{5/8}
d) R3C9 = 1, R2C9 = 3
e) 3 locked in 12(4) @ N1 = {1236} locked for N1, 3 locked for R1
f) 12(2) = [48/75]
g) Naked pair (47) locked in R2C15 for R2
h) 14(3) @ N3 <> 6,7 because R12C6 <> 2,6,7
i) Killer pair (89) locked in 14(3) @ R1C6 + R1C5 for N2
j) 8,9 locked in R3C123 for N1
7. N1
a) 22(4): R1C3 <> 4 because (89) only possible @ R1C5 and R1C45+R2C4 <> 7
b) 12(2) = {48} because R1C3 = (57) blocks {57} -> R2C1 = 4, R3C1 = 8
8. C123
a) 14(2) = {59} locked for C1+N7
b) 22(3) = {679} -> R6C2 = 9
c) Hidden Single: R3C3 = 9 @ C3
d) 18(3) = 9{36/45}
9. N3
a) 2 locked in R3C78
b) 14(3) = 1{49/58} -> 1 locked for C6+N2
c) R6C6 = 5, R6C5 = 1
10. N8
a) 7(2) = {25} locked
b) R9C5 = 6
c) 15(3) = 4{29/38}
d) Hidden Single: R7C4 = 1
e) 14(4) = must have 6,7 xor 8 and it's only possible @ R6C3 -> R6C3 = (678)
11. R45
a) 2 locked in 11(3) @ N4 = {245} locked for R5+N4 -> R5C1 = 2
b) 11(3) @ N6 = {137} locked for N6, R5C9 = 7
c) 18(3) @ N4 = {369}
12. C456
a) Killer pair (34) locked in 15(3) + R6C4 for C4
b) 18(3) @ C4 = {369} -> R3C4 = 6, R4C3 = 3
c) 22(4) = {2578} -> R1C3 = 7, R1C5 = 8
d) 14(3) @ C6 = {149} -> R1C7 = 4, {19} locked for C6
e) 9 locked in 15(3) @ N8 = {249} -> R9C3 = 2, (49) locked C4+N8
f) 18(4) = {1368} -> R9C7 = 1, (38) locked for C6
g) 18(3) @ N8 = 7{29/38/56} -> R7C6 = 7, R7C7 <> 2,6,8
h) 16(3) = {457} -> R3C6 = 4, R3C7 = 7, R4C7 = 5
13. R678
a) R7C2 = 6, R7C3 = 4
b) 14(4) = {1346} -> R6C3 = 6, R6C4 = 3
c) 10(2) = {28} locked for C9+N9
14. Rest is singles.
Rating: 1.0. Only (simple) Innies+Outies and Killer pairs were needed to solve this one.
A81 Walkthrough:
1. N5+C5
a) Innies R5 = 23(3) = {689} locked for R5+N5; R5C6 = 6
b) 8(2) = [26] -> R4C6 = 2
c) 30(5) = {15789} locked for N5
d) 7(2) <> 3,4 because R4C5 = (34)
e) 14(3) <> 5,6 because R4C5 = (34) and {356} blocked by Killer pair (56) of 7(2)
2. C6789
a) 4(2) = {13} locked for C9+N3
b) 28(4) = 89{47/56}; (89) locked for N3
c) 10(2) <> 7,9
d) Innies+Outies: 1 = R9C5 - R6C6 -> R9C5 = (268)
3. R1234
a) Innies R1234 = 7 = R4C4
b) Innies R12 = 14(3): R2C15 <> 1,3 because R2C9 = (13)
c) Innies N1 = 21(3) <> 1,2,3
d) 12(2): R3C1 <> 9
4. C45
a) 7 locked in R123C5 for N2
b) Innies+Outies C1234: R1C5 = R5C4 = (89)
c) Naked pair (89) locked for R15C5 for C5
d) 14(3) = {347}
e) 2,6 locked in R123C4 for C4
5. N7+R6
a) 30(5) = {15789} -> 1,5 locked for R6
b) Innies N7 = 12(3): R79C3 <> 7,8,9 because R7C2 >= 5
c) Innies N7 = 12(3): R79C3 <> 5,6 because {156} blocked by Killer pair (56) of 14(2)
6. ! R12
a) Innies R12 = 14(3) = 4{19/37}, 4 locked for R2
b) 12(2): R3C1 <> 4,7
c) ! Innies+Outies R12: 2 = R3C19 - R2C5; R2C5 = (47)
-> R3C19 = 6/9(2) = 1{5/8}
d) R3C9 = 1, R2C9 = 3
e) 3 locked in 12(4) @ N1 = {1236} locked for N1, 3 locked for R1
f) 12(2) = [48/75]
g) Naked pair (47) locked in R2C15 for R2
h) 14(3) @ N3 <> 6,7 because R12C6 <> 2,6,7
i) Killer pair (89) locked in 14(3) @ R1C6 + R1C5 for N2
j) 8,9 locked in R3C123 for N1
7. N1
a) 22(4): R1C3 <> 4 because (89) only possible @ R1C5 and R1C45+R2C4 <> 7
b) 12(2) = {48} because R1C3 = (57) blocks {57} -> R2C1 = 4, R3C1 = 8
8. C123
a) 14(2) = {59} locked for C1+N7
b) 22(3) = {679} -> R6C2 = 9
c) Hidden Single: R3C3 = 9 @ C3
d) 18(3) = 9{36/45}
9. N3
a) 2 locked in R3C78
b) 14(3) = 1{49/58} -> 1 locked for C6+N2
c) R6C6 = 5, R6C5 = 1
10. N8
a) 7(2) = {25} locked
b) R9C5 = 6
c) 15(3) = 4{29/38}
d) Hidden Single: R7C4 = 1
e) 14(4) = must have 6,7 xor 8 and it's only possible @ R6C3 -> R6C3 = (678)
11. R45
a) 2 locked in 11(3) @ N4 = {245} locked for R5+N4 -> R5C1 = 2
b) 11(3) @ N6 = {137} locked for N6, R5C9 = 7
c) 18(3) @ N4 = {369}
12. C456
a) Killer pair (34) locked in 15(3) + R6C4 for C4
b) 18(3) @ C4 = {369} -> R3C4 = 6, R4C3 = 3
c) 22(4) = {2578} -> R1C3 = 7, R1C5 = 8
d) 14(3) @ C6 = {149} -> R1C7 = 4, {19} locked for C6
e) 9 locked in 15(3) @ N8 = {249} -> R9C3 = 2, (49) locked C4+N8
f) 18(4) = {1368} -> R9C7 = 1, (38) locked for C6
g) 18(3) @ N8 = 7{29/38/56} -> R7C6 = 7, R7C7 <> 2,6,8
h) 16(3) = {457} -> R3C6 = 4, R3C7 = 7, R4C7 = 5
13. R678
a) R7C2 = 6, R7C3 = 4
b) 14(4) = {1346} -> R6C3 = 6, R6C4 = 3
c) 10(2) = {28} locked for C9+N9
14. Rest is singles.
Rating: 1.0. Only (simple) Innies+Outies and Killer pairs were needed to solve this one.
Last edited by Afmob on Fri Dec 21, 2007 5:37 am, edited 4 times in total.
Here's my walkthrough
I found this one not too difficult - but it required (at least for me) some significant combo crunching. I'd rate it a 1.25.
Edited for typo - Thanks Afmob!
Reworked - I took an elimination too early. I have moved things around to fix this.
Assassin 81 walkthrough
Preliminaries:
a. 12(4)n1 = {1236/1245} (no 7..9) -> 1,2 locked for n1
b. 12(2)n1 = {39/48/57} (no 6)
c. 28(4)n3 = {4789/5689} (no 1..3) -> 8,9 locked for n3
d. 4(2)n3 = {13} (no 2,4..7) -> 1,3 locked for n3 and c9
e. 11(3)n4 and n6 = {128/137/146/236/245} (no 9) -> 9 in r5 locked in n5 -> no 9 elsewhere in n5
f. 22(3)n47 = {589/679} (no 1..4) -> r4c2 no 9 (CPE)
g. 14(4)n4578 = {1238/1247/1256/1346/2345} (no 9)
h. 8(2)n5 = {17/26/35} (no 4,8,9)
i. 14(2)n7 = {59/68} (no 1..4,7)
j. 7(2)n8 = {16/25/34} (no 7..9)
k. 10(2)n9 = {28/46} (no 5,7,9)
1. Innies r5: r5c456 = 23(3) = {89}[6]
1a. -> {89} locked for n5 -> no 8,9 elsewhere in n5 and r5
1b. -> r4c6 = 2
1c. 11(3)n4 and n6 = {137/245}
2. Innie r1234: r4c4 = 7
2a. Innie n5: r4c5+r6c4 = 7(2) = {34} -> locked for n5
2b. r6c56 = {15} -> locked for r6
2c. 7(2)n8 no 3,4 (blocked by r4c5
2d. killer pair {15} in 7(2)n8 and r6c5 -> no 1,5 elsewhere in c5
2e. 22(3)n47: r7c2 no 8 (as there is no 5 in r6c12)
3. Innies n1: r1c3+r3c23 = 21(3) = {489/579/678} (no 3)
This is where I originally took an early elimination. I’m going to move some steps around to make it work. I am leaving the same numbering
4. 8 locked in c1 in 12(2)n1 and 14(2)n7 -> no 8 elsewhere in c1
5. Innie and Outtie c1234: r1c5 = r5c4
5a. -> r1c5 no 2,3,4,6,7
5b. pair {89} in r15c5 -> no 8,9 elsewhere in c5
5c. 14(3)n25 = {347} -> locked for c5; 7 locked for n2
5d. 2,6 in n2 locked in c4 -> no 2,6 elsewhere in c4
6. 22(4)n12 contains at least one of {26} and at least one of {89}
6a. 22(4)n12 = {1678/2389/2479/2569/2578/3469/3568}
6b. -> r12c4 no 8,9 (if there is both 8 and 9 in 22(4)n12 then it is in r1c3)
7. 14(3)n23 = {1[4]9}/{1[5]8}/{3[2]9}/{4[2]8}/{3[6]5}
Note: {3[7]4} blocked by r23c5
7a. -> r1c7 no 7
8. Innies r12: r2c159 = 14(3) = [473/743] -> 4 locked in r2c156 for r2
Note: combo [941] blocked as this would place 3s in r3c19
8a. -> r2c1 = {47} no 3,5,8,9
8b. -> r2c5 = {47} no 3 -> {47} locked for r2, no 4,7 elsewhere in r2
8c. -> r2c9 = 3
8d. -> r3c9 = 1
8c. -> r3c1 no 3,4,7,9
8d -8g. -> deleted, these were repeat statements I had already made above
Here's where I moved the rest of step 3. I couldn't put it as early as I originally had. Thanks Afmob for pointing this out!!
3a. -> 3 locked in 12(4)n1 in r1 -> no 3 elsewhere in r1
3b. -> 12(4)n1 = {1236} (no 4,5) -> 6 locked in 12(4)n1
9. Innies r89: r8c159 = 16(3) = [916/952/628/826/862]
9a. -> r8c1 no 5
9b. -> r7c1 no 9
9c. -> r8c9 no 4
9d. -> r7c9 no 6
10. Innies n7: r7c23+r9c3 = 12(3)
10a. -> min r7c2 = 5 -> max r79c3 = 7(2) (no 7,8,9)
11. 19(4)n7 = {1279/1378/1459/1468/2359/2368/3457}
Note: combos {1369/1567/2458} blocked by 14(2)n7 and combo {2467} blocked by 14(2)n7 + r7c2
11a. -> 5,6 locked in n7 in 19(4)n7 and 14(2)n7 and r7c2
11b. -> r79c3 no 5,6
12. 15(3)n78 = [1]{59}/[2]{49}/[3]{48}/[4]{38}
Note: [2]{58} blocked by 7(2)n8 and r9c5
12a. -> r89c4 no 1
12b. killer pair {89} locked in c4 in 15(3)n78 and r5c4 -> no 8,9 elsewhere in c4
13. 14(3)n14 = [491/518/716/761/536/563]
Note: combos [9]{14} / [8]{15} / [7]{34} blocked by 11(3)n4
13a. -> r3c2 = {457} no 8,9
13b. -> 11(3)n4 = {245} (combo {137} blocked by 14(3)n14
13c. -> {245} locked in n2 and r5
13d. -> 11(3)n6 = {13}[7] -> locked for n6
13e. 9 in c3 locked in n1 -> no 9 elsewhere in c3
14. h21(3)n1 -> r13c3 no 4 (needs both 8 and 9)
15. 17(3)n36 = [2]{69}/[4]{58}/[5]{48}/[7]{46}
15a. -> r3c8 no 6
16. Outies c12: r258c3 = 14(3) = [158/248/257/653]
16a. -> r5c3 no 2
16b. -> r8c3 no 1,2,4,5,6
17. Outies c89: r258c7 = 17(3) = [917/539/935/638/836]
17a. -> r8c7 no 1,2,3,4
18. 15(3)n69 = {68}[1]/{249}/{28}[5]/{26}[7]/{48}[3]/{46}[5]
18a. -> r7c8 no 6,8
19. 18(3)n124
19a. -> max r3c34 = 15 -> min r4c3 = 3 (no 1)
19b. -> 1 locked in n4 in 14(3)n14 = [4]{19}/[518]/[7]{16}
19c. -> r4c12 no 3
19d. -> 3 in n4 locked in c3 -> no 3 elsewhere in c3
20. Innies n7: r7c2 no 5 (max of r79c3 = 6, min r7c2 = 6)
20a. 22n47 = {679} -> no 8
20b. -> r4c2 no 6 (CPE)
21. 22(4)n12 = [7186/7681/7492/5296/5692/7285/7582]
Note: [7{16}8] blocked by 18(3)n124 as r3c4 = 2 and requires a 7 which is blocked
21a. -> r1c3 no 8,9
21b. -> single: r3c3 = 9
21c. -> single r3c1 = 8
21d. -> r2c1 = 4
21e. -> r2c5 = 7
22. 18(3)n124 = [936/963]
22a. -> r3c4 no 2,4,5
22b. -> r4c3 no 8
22c. -> 2 in n2 locked in 22(4) -> no 1
22d. -> 1 in n2 locked in c6 -> no 1 elsewhere in c6
singles and cage sums to the end
I found this one not too difficult - but it required (at least for me) some significant combo crunching. I'd rate it a 1.25.
Edited for typo - Thanks Afmob!
Reworked - I took an elimination too early. I have moved things around to fix this.
Assassin 81 walkthrough
Preliminaries:
a. 12(4)n1 = {1236/1245} (no 7..9) -> 1,2 locked for n1
b. 12(2)n1 = {39/48/57} (no 6)
c. 28(4)n3 = {4789/5689} (no 1..3) -> 8,9 locked for n3
d. 4(2)n3 = {13} (no 2,4..7) -> 1,3 locked for n3 and c9
e. 11(3)n4 and n6 = {128/137/146/236/245} (no 9) -> 9 in r5 locked in n5 -> no 9 elsewhere in n5
f. 22(3)n47 = {589/679} (no 1..4) -> r4c2 no 9 (CPE)
g. 14(4)n4578 = {1238/1247/1256/1346/2345} (no 9)
h. 8(2)n5 = {17/26/35} (no 4,8,9)
i. 14(2)n7 = {59/68} (no 1..4,7)
j. 7(2)n8 = {16/25/34} (no 7..9)
k. 10(2)n9 = {28/46} (no 5,7,9)
1. Innies r5: r5c456 = 23(3) = {89}[6]
1a. -> {89} locked for n5 -> no 8,9 elsewhere in n5 and r5
1b. -> r4c6 = 2
1c. 11(3)n4 and n6 = {137/245}
2. Innie r1234: r4c4 = 7
2a. Innie n5: r4c5+r6c4 = 7(2) = {34} -> locked for n5
2b. r6c56 = {15} -> locked for r6
2c. 7(2)n8 no 3,4 (blocked by r4c5
2d. killer pair {15} in 7(2)n8 and r6c5 -> no 1,5 elsewhere in c5
2e. 22(3)n47: r7c2 no 8 (as there is no 5 in r6c12)
3. Innies n1: r1c3+r3c23 = 21(3) = {489/579/678} (no 3)
This is where I originally took an early elimination. I’m going to move some steps around to make it work. I am leaving the same numbering
4. 8 locked in c1 in 12(2)n1 and 14(2)n7 -> no 8 elsewhere in c1
5. Innie and Outtie c1234: r1c5 = r5c4
5a. -> r1c5 no 2,3,4,6,7
5b. pair {89} in r15c5 -> no 8,9 elsewhere in c5
5c. 14(3)n25 = {347} -> locked for c5; 7 locked for n2
5d. 2,6 in n2 locked in c4 -> no 2,6 elsewhere in c4
6. 22(4)n12 contains at least one of {26} and at least one of {89}
6a. 22(4)n12 = {1678/2389/2479/2569/2578/3469/3568}
6b. -> r12c4 no 8,9 (if there is both 8 and 9 in 22(4)n12 then it is in r1c3)
7. 14(3)n23 = {1[4]9}/{1[5]8}/{3[2]9}/{4[2]8}/{3[6]5}
Note: {3[7]4} blocked by r23c5
7a. -> r1c7 no 7
8. Innies r12: r2c159 = 14(3) = [473/743] -> 4 locked in r2c156 for r2
Note: combo [941] blocked as this would place 3s in r3c19
8a. -> r2c1 = {47} no 3,5,8,9
8b. -> r2c5 = {47} no 3 -> {47} locked for r2, no 4,7 elsewhere in r2
8c. -> r2c9 = 3
8d. -> r3c9 = 1
8c. -> r3c1 no 3,4,7,9
8d -8g. -> deleted, these were repeat statements I had already made above
Here's where I moved the rest of step 3. I couldn't put it as early as I originally had. Thanks Afmob for pointing this out!!
3a. -> 3 locked in 12(4)n1 in r1 -> no 3 elsewhere in r1
3b. -> 12(4)n1 = {1236} (no 4,5) -> 6 locked in 12(4)n1
9. Innies r89: r8c159 = 16(3) = [916/952/628/826/862]
9a. -> r8c1 no 5
9b. -> r7c1 no 9
9c. -> r8c9 no 4
9d. -> r7c9 no 6
10. Innies n7: r7c23+r9c3 = 12(3)
10a. -> min r7c2 = 5 -> max r79c3 = 7(2) (no 7,8,9)
11. 19(4)n7 = {1279/1378/1459/1468/2359/2368/3457}
Note: combos {1369/1567/2458} blocked by 14(2)n7 and combo {2467} blocked by 14(2)n7 + r7c2
11a. -> 5,6 locked in n7 in 19(4)n7 and 14(2)n7 and r7c2
11b. -> r79c3 no 5,6
12. 15(3)n78 = [1]{59}/[2]{49}/[3]{48}/[4]{38}
Note: [2]{58} blocked by 7(2)n8 and r9c5
12a. -> r89c4 no 1
12b. killer pair {89} locked in c4 in 15(3)n78 and r5c4 -> no 8,9 elsewhere in c4
13. 14(3)n14 = [491/518/716/761/536/563]
Note: combos [9]{14} / [8]{15} / [7]{34} blocked by 11(3)n4
13a. -> r3c2 = {457} no 8,9
13b. -> 11(3)n4 = {245} (combo {137} blocked by 14(3)n14
13c. -> {245} locked in n2 and r5
13d. -> 11(3)n6 = {13}[7] -> locked for n6
13e. 9 in c3 locked in n1 -> no 9 elsewhere in c3
14. h21(3)n1 -> r13c3 no 4 (needs both 8 and 9)
15. 17(3)n36 = [2]{69}/[4]{58}/[5]{48}/[7]{46}
15a. -> r3c8 no 6
16. Outies c12: r258c3 = 14(3) = [158/248/257/653]
16a. -> r5c3 no 2
16b. -> r8c3 no 1,2,4,5,6
17. Outies c89: r258c7 = 17(3) = [917/539/935/638/836]
17a. -> r8c7 no 1,2,3,4
18. 15(3)n69 = {68}[1]/{249}/{28}[5]/{26}[7]/{48}[3]/{46}[5]
18a. -> r7c8 no 6,8
19. 18(3)n124
19a. -> max r3c34 = 15 -> min r4c3 = 3 (no 1)
19b. -> 1 locked in n4 in 14(3)n14 = [4]{19}/[518]/[7]{16}
19c. -> r4c12 no 3
19d. -> 3 in n4 locked in c3 -> no 3 elsewhere in c3
20. Innies n7: r7c2 no 5 (max of r79c3 = 6, min r7c2 = 6)
20a. 22n47 = {679} -> no 8
20b. -> r4c2 no 6 (CPE)
21. 22(4)n12 = [7186/7681/7492/5296/5692/7285/7582]
Note: [7{16}8] blocked by 18(3)n124 as r3c4 = 2 and requires a 7 which is blocked
21a. -> r1c3 no 8,9
21b. -> single: r3c3 = 9
21c. -> single r3c1 = 8
21d. -> r2c1 = 4
21e. -> r2c5 = 7
22. 18(3)n124 = [936/963]
22a. -> r3c4 no 2,4,5
22b. -> r4c3 no 8
22c. -> 2 in n2 locked in 22(4) -> no 1
22d. -> 1 in n2 locked in c6 -> no 1 elsewhere in c6
singles and cage sums to the end
Last edited by Caida on Sat Dec 22, 2007 5:50 am, edited 3 times in total.
A nice one and not too many innies and outies which have been necessary lately.
Prelims
1.r5c456={89}6 r4c6=2
2.I r6-9 r6c56=6={15} so r4c4=7 and r4c5,r6c4={34}
3.I-O c6-9 r9c5=r6c4+1=2/6
4.7(2) cage N8 <>{34} (point 2) therefore r6789c5 =naked quadruple [1256} so r1c5=8/9 r23c5=7. 14(3) cage N25={347}
5.R2C159=14 and combo restrictions mean r2c9=3,r3c9=1 (if r2c9=1 r2c5 <>7 (would put r2c1=6) <>3 (then r2c159<>14) and also <>4 (this would put r2c1=9,r3c1=3...then two 3s in r3).
6.Thus 12(2) cage N1 <>{39} so 12(4) cage N1={1236}
7.In r5 the two 11(2) cages must be 137/245 -> 1/4,1/5
8.Thus r3c2 <>8 or 9 as then r4c12 combos conflict with 11(2) 1/4,1/5 requirements.
9.If r3c2=4 r4c12=91 and placements in r23,r78 c1 mean no number can go at r6c1.So r3c2=5/7 and r23c1=48 -> r5c2=7.r78c1={59} so r6c2=9
10.Now both 7 and 9 look at r4c3 so r3c4<>2 so in N2 2 at r12c4.
11.In N2 1 at r12c6 so r6c6=5 r6c5=1 r78c5={25} r9c5=6
12.In r4 c7<>9 as then 16(3) cage N236 cannot be completed.So 9 at r4c8/9.17(3) cage N36 r3c8r4c89=7{19}/2{69}->1/6
13.Thus r4c12<>7 ie<>16(point 12) or 25,34 thus r3c2=5
14.r4c12=18/[36} so 11(2) N4 <> 137 so =245
mop up now
Not too difficult..??? about 1.25??
Regards
Gary
Prelims
1.r5c456={89}6 r4c6=2
2.I r6-9 r6c56=6={15} so r4c4=7 and r4c5,r6c4={34}
3.I-O c6-9 r9c5=r6c4+1=2/6
4.7(2) cage N8 <>{34} (point 2) therefore r6789c5 =naked quadruple [1256} so r1c5=8/9 r23c5=7. 14(3) cage N25={347}
5.R2C159=14 and combo restrictions mean r2c9=3,r3c9=1 (if r2c9=1 r2c5 <>7 (would put r2c1=6) <>3 (then r2c159<>14) and also <>4 (this would put r2c1=9,r3c1=3...then two 3s in r3).
6.Thus 12(2) cage N1 <>{39} so 12(4) cage N1={1236}
7.In r5 the two 11(2) cages must be 137/245 -> 1/4,1/5
8.Thus r3c2 <>8 or 9 as then r4c12 combos conflict with 11(2) 1/4,1/5 requirements.
9.If r3c2=4 r4c12=91 and placements in r23,r78 c1 mean no number can go at r6c1.So r3c2=5/7 and r23c1=48 -> r5c2=7.r78c1={59} so r6c2=9
10.Now both 7 and 9 look at r4c3 so r3c4<>2 so in N2 2 at r12c4.
11.In N2 1 at r12c6 so r6c6=5 r6c5=1 r78c5={25} r9c5=6
12.In r4 c7<>9 as then 16(3) cage N236 cannot be completed.So 9 at r4c8/9.17(3) cage N36 r3c8r4c89=7{19}/2{69}->1/6
13.Thus r4c12<>7 ie<>16(point 12) or 25,34 thus r3c2=5
14.r4c12=18/[36} so 11(2) N4 <> 137 so =245
mop up now
Not too difficult..??? about 1.25??
Regards
Gary
I had only just started A81 when Afmob, in a message about another walkthrough, commented that it's easier using innies/outies and asked what I thought about the posted ratings?
Since I'd only done Prelims and about 15 steps I had another look at innies/outies and managed to find the key one which I've inserted as step 10. Thanks Afmob.
It definitely makes the solution quicker and easier. I therefore rate A81 as 1.0.
Here is my walkthrough
Prelims
a) R23C1 = {39/48/57}, no 1,2,6
b) R45C4 = {17/26/35}, no 4,8,9
c) R78C1 = {59/68}
d) R78C5 = {16/25/34}, no 7,8,9
e) R78C9 = {19/28/37/46}, no 5
f) R23C9 = {13}, locked for C9 and N3, clean-up: no 7,9 in R78C9
g) R5C123 = {128/137/146/236/245}, no 9
h) R5C789 = {128/137/146/236/245}, no 9
i) 22(3) cage at R6C1 = 9{58/67}, CPE no 9 in R4C2
j) 12(4) cage in N1 = {1236/1245}, 1,2 locked for N1
k) 28(4) cage in N3 = {4789/5689}, 8,9 locked for N3
l) 14(4) cage at R6C3 = {1238/1247/1256/1346/2345}, no 9
1. 45 rule on R5 3 innies R5C456 = 23 = {689} -> R5C6 = 6, R4C6 = 2, R5C45 = {89}, locked for R5 and N5
1a. 30(5) cage in N5 = {15789} (only remaining combination), locked for N5
1b. 45 rule on R6789 2 innies R6C56 = 6 = {15}, locked for R6 and N5 -> R4C4 = 7
1c. R6C89 = [34] clashes with R6C4 -> no 8 in R7C8
1d. R5C123 = {137/245}
1e. R5C789 = {137/245}
2. R78C5 = {16/25} (cannot be {34} which clashes with R4C5), no 3,4
3. 45 rule on C6789 1 outie R9C5 = 1 innie R6C6 + 1, R9C5 = {26}
4. Naked quad {1256} in R6789C5, locked for C5
4a. Killer pair 2,6 in R78C5 and R9C5, locked for N8
4b. 7 in C5 locked in R123C5, locked for N2
5. R234C5 = {347} (only remaining combination), locked for C5
6. 22(3) cage at R6C1 = 9{58/67}
6a. 5 of {589} must be in R7C2 -> no 8 in R7C2
7. 45 rule on N1 3 innies R1C3 + R3C23 = 21 = {489/579/567}, no 3
8. 45 rule on R12 3 innies R2C159 = 14 = {149/347} (cannot be {158} because 5,8 only in R2C1), no 5,8, 4 locked for R2, clean-up: no 4,7 in R3C1
8a. 3 of {347} must be in R2C9 -> no 3 in R2C15, clean-up: no 9 in R3C1
9. 45 rule on R89 3 innies R8C159 = 16 = {169/259/268}, no 4, clean-up: no 6 in R7C9
9a. 9 of {259} must be in R8C1 -> no 5 in R8C1, clean-up: no 9 in R7C1
10. 45 rule on R12 2 outies R3C19 = 1 innie R2C5 + 2
10a. R2C5 = {47} -> R3C19 = 6,9 = [51/81] (cannot be [33]) -> R3C1 = {58}, R3C9 = 1, R2C9 = 3, clean-up: no 9 in R2C1
10b. Naked pair {47} in R2C15, locked for R2
11. 3 in N1 locked in R1C12, locked for R1
11a. 12(4) cage in N1 = {1236}, locked for N1
12. Killer pair 5,8 in R3C1 and R78C1, locked for C1
13. 45 rule on N7 3 innies R7C23 + R9C3 = 12 = {129/147/237/246/345} (cannot be {138} because no 1,3,8 in R7C2, cannot be {156} which clashes with R78C1), no 8
13a. 5,6,7,9 must be in R7C2 -> no 5,6,7,9 in R79C3
14. 15(3) cage at R8C4 = {159/249/258/348}
14a. 1 of {159} must be in R9C3 -> no 1 in R89C4
15. Killer pair 8,9 in R5C4 and R89C4, locked for C4
16. 14(3) cage at R3C2 = {149/158/167/347/356}
16a. 8 of {158} must be in R4C12 (cannot be [815] which clashes with R5C123)
16b. 9 of {149} must be in R4C1 (cannot be 9{14} which clashes with R5C123)
16c. -> no 8,9 in R3C2
16d. 5 of {158/356} must be in R3C2 -> no 5 in R4C2
17. R1C3 + R3C23 (step 7) = {489/579/567}
17a. 4 of {489} must be in R3C2 -> no 4 in R13C3
18. 14(3) cage at R1C6 = {149/158/248} (cannot be {167/257} because 2,6,7 only in R1C7), no 6,7
18a. 5 of {158} must be in R1C7 -> no 5 in R12C6
18a. Killer pair 8,9 in R1C5 and R12C6, locked for N2
19. 8,9 in R3 locked in R3C13 -> R3C1 = 8, R3C3 = 9, R2C1 = 4, R2C5 = 7, clean-up: no 6 in R78C1 -> R78C1 = [59], clean-up: no 2 in R8C5
20. R6C2 = 9 (hidden single in C2)
20a. R6C1 + R7C2 = {67}, CPE no 6,7 in R45C2
21. R8C59 (step 9) = {16/25}, no 8, clean-up: no 2 in R7C9
21a. 6 of {16} must be in R8C9 -> no 6 in R8C5, clean-up: no 1 in R7C5
22. R3C3 = 9 -> R3C4 + R4C3 = 9 = {36/45}, no 1,2,8
22a. 2 in R3 locked in R3C78, locked for N3
23. 14(3) cage at R1C6 (step 18) = {149/158}, 1 locked in R12C6, locked for C6 and N2 -> R6C56 = [15], R8C5 = 5, R7C5 = 2, R9C5 = 6
23a. 4 of {149} must be in R1C7 -> no 4 in R1C6
23b. R7C4 = 1 (hidden single in C4)
24. Naked pair {34} in R3C56, locked for R3 and N2, clean-up: no 5,6 in R4C3 (step 22)
24a. Naked pair {34} in R4C35, locked for R4
25. 14(4) cage at R6C3 = {1238/1247/1346}
25a. 6,7,8 must be in R6C3 -> R6C3 = {678}
26. 2 in N5 locked in R5C123 = {245} (step 1d) -> R5C1 = 2, R5C23 = {45}, locked for R5 and N4 -> R5C9 = 7, R4C3 = 3, R3C4 = 6 (step 22), R34C5 = [34], R3C6 = 4, R6C4 = 3, R7C3 = 4, R6C3 = 6 (step 25), R6C1 = 7, R7C2 = 6, R5C23 = [45], R1C3 = 7, R3C2 = 5, R78C9 = [82], R6C9 = 4
26a. Naked pair {13} in R5C78, locked for N6
26b. Naked pair {28} in R6C78, locked for N6
27. Naked triple {569} in R4C789, locked for R4 -> R4C1 = 1, R4C2 = 8, R9C1 = 3, R1C1 = 6
28. R8C3 = 8 (hidden single in C3), R8C4 = 4
29. Naked pair {12} in R2C23, locked for R2 and N1 -> R1C2 = 3, R12C4 = [25], R1C5 = 8 {cage sum), R12C6 = [19], R1C7 = 4 (step 23), R5C45 = [89], R9C4 = 9, R9C3 = 2 (step 14), R2C23 = [21], R9C9 = 5, R1C89 = [59], R4C89 = [96], R4C7 = 5
30. R89C6 cannot be {78} -> R789C6 = [738]
and the rest is naked singles and cage sums
Since I'd only done Prelims and about 15 steps I had another look at innies/outies and managed to find the key one which I've inserted as step 10. Thanks Afmob.
It definitely makes the solution quicker and easier. I therefore rate A81 as 1.0.Here is my walkthrough
Prelims
a) R23C1 = {39/48/57}, no 1,2,6
b) R45C4 = {17/26/35}, no 4,8,9
c) R78C1 = {59/68}
d) R78C5 = {16/25/34}, no 7,8,9
e) R78C9 = {19/28/37/46}, no 5
f) R23C9 = {13}, locked for C9 and N3, clean-up: no 7,9 in R78C9
g) R5C123 = {128/137/146/236/245}, no 9
h) R5C789 = {128/137/146/236/245}, no 9
i) 22(3) cage at R6C1 = 9{58/67}, CPE no 9 in R4C2
j) 12(4) cage in N1 = {1236/1245}, 1,2 locked for N1
k) 28(4) cage in N3 = {4789/5689}, 8,9 locked for N3
l) 14(4) cage at R6C3 = {1238/1247/1256/1346/2345}, no 9
1. 45 rule on R5 3 innies R5C456 = 23 = {689} -> R5C6 = 6, R4C6 = 2, R5C45 = {89}, locked for R5 and N5
1a. 30(5) cage in N5 = {15789} (only remaining combination), locked for N5
1b. 45 rule on R6789 2 innies R6C56 = 6 = {15}, locked for R6 and N5 -> R4C4 = 7
1c. R6C89 = [34] clashes with R6C4 -> no 8 in R7C8
1d. R5C123 = {137/245}
1e. R5C789 = {137/245}
2. R78C5 = {16/25} (cannot be {34} which clashes with R4C5), no 3,4
3. 45 rule on C6789 1 outie R9C5 = 1 innie R6C6 + 1, R9C5 = {26}
4. Naked quad {1256} in R6789C5, locked for C5
4a. Killer pair 2,6 in R78C5 and R9C5, locked for N8
4b. 7 in C5 locked in R123C5, locked for N2
5. R234C5 = {347} (only remaining combination), locked for C5
6. 22(3) cage at R6C1 = 9{58/67}
6a. 5 of {589} must be in R7C2 -> no 8 in R7C2
7. 45 rule on N1 3 innies R1C3 + R3C23 = 21 = {489/579/567}, no 3
8. 45 rule on R12 3 innies R2C159 = 14 = {149/347} (cannot be {158} because 5,8 only in R2C1), no 5,8, 4 locked for R2, clean-up: no 4,7 in R3C1
8a. 3 of {347} must be in R2C9 -> no 3 in R2C15, clean-up: no 9 in R3C1
9. 45 rule on R89 3 innies R8C159 = 16 = {169/259/268}, no 4, clean-up: no 6 in R7C9
9a. 9 of {259} must be in R8C1 -> no 5 in R8C1, clean-up: no 9 in R7C1
10. 45 rule on R12 2 outies R3C19 = 1 innie R2C5 + 2
10a. R2C5 = {47} -> R3C19 = 6,9 = [51/81] (cannot be [33]) -> R3C1 = {58}, R3C9 = 1, R2C9 = 3, clean-up: no 9 in R2C1
10b. Naked pair {47} in R2C15, locked for R2
11. 3 in N1 locked in R1C12, locked for R1
11a. 12(4) cage in N1 = {1236}, locked for N1
12. Killer pair 5,8 in R3C1 and R78C1, locked for C1
13. 45 rule on N7 3 innies R7C23 + R9C3 = 12 = {129/147/237/246/345} (cannot be {138} because no 1,3,8 in R7C2, cannot be {156} which clashes with R78C1), no 8
13a. 5,6,7,9 must be in R7C2 -> no 5,6,7,9 in R79C3
14. 15(3) cage at R8C4 = {159/249/258/348}
14a. 1 of {159} must be in R9C3 -> no 1 in R89C4
15. Killer pair 8,9 in R5C4 and R89C4, locked for C4
16. 14(3) cage at R3C2 = {149/158/167/347/356}
16a. 8 of {158} must be in R4C12 (cannot be [815] which clashes with R5C123)
16b. 9 of {149} must be in R4C1 (cannot be 9{14} which clashes with R5C123)
16c. -> no 8,9 in R3C2
16d. 5 of {158/356} must be in R3C2 -> no 5 in R4C2
17. R1C3 + R3C23 (step 7) = {489/579/567}
17a. 4 of {489} must be in R3C2 -> no 4 in R13C3
18. 14(3) cage at R1C6 = {149/158/248} (cannot be {167/257} because 2,6,7 only in R1C7), no 6,7
18a. 5 of {158} must be in R1C7 -> no 5 in R12C6
18a. Killer pair 8,9 in R1C5 and R12C6, locked for N2
19. 8,9 in R3 locked in R3C13 -> R3C1 = 8, R3C3 = 9, R2C1 = 4, R2C5 = 7, clean-up: no 6 in R78C1 -> R78C1 = [59], clean-up: no 2 in R8C5
20. R6C2 = 9 (hidden single in C2)
20a. R6C1 + R7C2 = {67}, CPE no 6,7 in R45C2
21. R8C59 (step 9) = {16/25}, no 8, clean-up: no 2 in R7C9
21a. 6 of {16} must be in R8C9 -> no 6 in R8C5, clean-up: no 1 in R7C5
22. R3C3 = 9 -> R3C4 + R4C3 = 9 = {36/45}, no 1,2,8
22a. 2 in R3 locked in R3C78, locked for N3
23. 14(3) cage at R1C6 (step 18) = {149/158}, 1 locked in R12C6, locked for C6 and N2 -> R6C56 = [15], R8C5 = 5, R7C5 = 2, R9C5 = 6
23a. 4 of {149} must be in R1C7 -> no 4 in R1C6
23b. R7C4 = 1 (hidden single in C4)
24. Naked pair {34} in R3C56, locked for R3 and N2, clean-up: no 5,6 in R4C3 (step 22)
24a. Naked pair {34} in R4C35, locked for R4
25. 14(4) cage at R6C3 = {1238/1247/1346}
25a. 6,7,8 must be in R6C3 -> R6C3 = {678}
26. 2 in N5 locked in R5C123 = {245} (step 1d) -> R5C1 = 2, R5C23 = {45}, locked for R5 and N4 -> R5C9 = 7, R4C3 = 3, R3C4 = 6 (step 22), R34C5 = [34], R3C6 = 4, R6C4 = 3, R7C3 = 4, R6C3 = 6 (step 25), R6C1 = 7, R7C2 = 6, R5C23 = [45], R1C3 = 7, R3C2 = 5, R78C9 = [82], R6C9 = 4
26a. Naked pair {13} in R5C78, locked for N6
26b. Naked pair {28} in R6C78, locked for N6
27. Naked triple {569} in R4C789, locked for R4 -> R4C1 = 1, R4C2 = 8, R9C1 = 3, R1C1 = 6
28. R8C3 = 8 (hidden single in C3), R8C4 = 4
29. Naked pair {12} in R2C23, locked for R2 and N1 -> R1C2 = 3, R12C4 = [25], R1C5 = 8 {cage sum), R12C6 = [19], R1C7 = 4 (step 23), R5C45 = [89], R9C4 = 9, R9C3 = 2 (step 14), R2C23 = [21], R9C9 = 5, R1C89 = [59], R4C89 = [96], R4C7 = 5
30. R89C6 cannot be {78} -> R789C6 = [738]
and the rest is naked singles and cage sums
Last edited by Andrew on Thu Dec 20, 2007 10:51 pm, edited 1 time in total.
I agree. I don't have access to my usual working environment at the moment, so did this one on paper using only rough pencilmarks, working out any necessary combinations by hand. So it can't be rated any higher than 1.0.Andrew wrote:I had another look at innies/outies and managed to find the key one... It definitely makes the solution quicker and easier. I therefore rate A81 as 1.0.
Although nothing spectacular, it's nice to have some Assassins that are just about easy enough to still be done in this way. (Unless your name's Gary, of course, in which case even 1.75-rated puzzles are not immune to this approach!
). And despite it being "easy", I still got stuck in a couple of places trying to find that "obvious" way forward...Cheers,
Mike
Mike