Assassin 82
Posted: Fri Dec 21, 2007 7:24 am
Thanks Ruud for another nice puzzle. As you say there are a few presents including some hidden in the branches of the Christmas Tree.
This one felt a bit harder than last week so I'll rate it at 1.25.
Here is my walkthrough. It's late so I haven't had time to check it. I'll do that tomorrow, hope there aren't any mistakes apart from typos.
Edit. Went through again in the morning. I've simplified from step 24 onward. Step 24 had been written before I inserted step 20a. I haven't colour coded the changes this time, hope that's not a problem for anyone.
Prelims
a) R3C67 = {17/26/35}, no 4,8,9
b) R9C34 = {13}, locked for R9
c) R9C67 = {49/58/67}, no 2
d) R123C1 = {389/479/569/578}, no 1,2
e) 21(3) cage at R2C4 = {489/579/678}, no 1,2,3
f) R234C8 = {123}, locked for C8
g) R456C1 = 1{25/34}, 1 locked for C1 and N4
h) 19(3) cage in N6 = {289/379/469/478/568}, no 1
i) R789C5 = {127/145/235} (cannot be {136} which clashes with R9C4), no 6,8,9
1. 45 rule on C1234 1 innie R4C4 = 4
1a. R34C5 = 11 = {29/38/56}, no 1,7
2. 45 rule on C1 3 innies R789C1 = 17
2a. Cage overlap R67C2 = R9C1 + 5
2b. IOU no 5 in R6C2
3. 45 rule on C9 3 innies R789C9 = 12
3a. Cage overlap R67C8 = R9C9 + 4
3b. IOU no 4 in R6C8
4. 45 rule on C12 2 innies R15C2 = 7 = [16]/{25/34}, no 7,8,9, no 6 in R1C2
5. 45 rule on C89 2 innies R15C8 = 17 = {89}, locked for C8
5a. 4 in C5 locked in R789C5, locked for N9, clean-up: no 9 in R9C6
6. 18(3) cage in N9 = {459/468/567} (cannot be {289} because 2,8,9 only in R9C9), no 2
7. 45 rule on C6789 3 innies R245C6 = 9 = {126/135/234}, no 7,8,9
7a. Min R45C6 = 4 (from 21(4) cage) -> no 6 in R2C6
7b. Max R45C6 = 8 -> min R56C5 = 13, no 1,2,3
8. 45 rule on N3 3 outies R13C6 + R4C8 = 10, max R13C6 = 9, no 9 in R1C6
9. 45 rule on N1 2 outies R1C4 + R4C2 = 1 innie R3C3 + 9, min R3C3 = 4 -> min R1C4 + R4C2 = 13, no 1,2,3
10. 16(4) cage at R6C8 = {1267/1357/1456/2347/2356} (cannot be {1249/1258/1348} because R67C8 must contain two of 4,5,6,7), no 8,9
10a. 7 of {1267/1357/2347} must be in R6C8 -> no 7 in R78C9
10b. Cannot be {1456} because R7C8 = 4, R78C9 = {15/16} clash with 18(3) cage
10c. -> 16(4) cage at R6C8 = {1267/1357/2347/2356}
10d. -> R78C9 = {123}, no 5,6
11. R789C9 = 12 (step 3) = {129/138/237} (cannot be {147/156/246} because R78C9 only contain 1,2,3) -> R9C9 = {789}
11a. 18(3) cage in N9 (step 6) = {459/468/567}
11b. R9C9 = {789} -> no 7 in R89C8
12. 45 rule on N4 3 innies R4C2 + R6C23 = 24 = {789}, locked for N4
13. R67C2 = R9C1 + 5 (step 2a), min R67C2 = 8 -> no 2 in R9C1
13a. Max R9C1 = 9 -> max R67C2 = 14, no 7,8,9 in R7C2
14. 45 rule on R9 2 outies R8C28 = 1 innie R9C5 + 7, min R9C5 = 2 -> min R8C28 = 9, no 1,2 in R8C2
15. 45 rule on N6 3 innies R4C8 + R6C78 = 11 = [137/146/236/245/317/326] -> R6C7 = {1234}
15a. Max R6C7 = 4 -> min R6C6 + R7C7 = 13, no 1,2,3
16. Hidden triple {123} in N9 -> R8C7 = {123}
16a. Max R8C7 = 3 -> min R78C6 = 15, R78C6 = {6789}
17. 45 rule on R789 2 innies R7C37 = 2 outies R6C28 + 3, min R6C28 = 12 -> min R7C37 = 15, R7C37 = {6789}
17a. R7C37 = 15,16,17 -> R6C28 = 12,13,14 = [75/76/85/86/95], no 7 in R6C8
18. R7C8 = 7 (hidden single in C8), clean-up: no 6 in R9C6
18a. Naked triple {689} in R7C367, locked for R7
19. R789C9 (step 11) = {129/138}, 1 locked in R78C9 for C9 and N9
20. 1 in N6 locked in R4C8 + R6C7
20a. R4C8 + R6C78 (step 15) = [146] (only remaining permutation)
20b. R6C6 + R7C7 = 13 = [58/76]
20c. R78C9 = {12} (step 10c), locked for C9 and N9, R8C7 = 3, clean-up: no 5 in R3C6
20d. R78C6 = [69/87/96], no 8 in R8C6
21. Naked pair {23} in R23C8, locked for N3, clean-up: no 6 in R3C6
21a. Naked pair {45} in R89C8, locked for N9, R9C9 = 9 (step 11a), clean-up: no 4,8 in R9C6
21b. Naked pair {68} in R79C7, locked for C7, clean-up: no 2 in R3C6
22. Naked quad {5789} in R6C2356, locked for R6 -> R6C9 = 3
22a. 5 locked in R6C56 for N5, clean-up: no 6 in R3C5 (step 1a)
22b. R45C9 = 12 = {57} (only remaining combination), locked for C9 and N6
22c. Naked pair {29} in R45C7, locked for C7 and N6, R5C8 = 8, R1C8 = 9
23. 23(4) cage at R5C4, max R67C3 + R6C4 = 19 -> no 1,2,3 in R5C4
24. 45 rule on R123 1 remaining outie R4C2 = 1 innie R3C5 + 6 -> R3C5 = {23}, R4C2 = {89}, clean-up: no 2,3,6 in R4C5 (step 1)
24a. Naked pair {89} in R4C25, locked for R4 -> R45C7 = [29]
25. Hidden triple {123} in R45C6 + R6C4, no 6 in R45C6 -> R4C6 = 3, R4C1 = 5, R4C3 = 6, R45C9 = [75], clean-up: no 5 in R3C7
25a. R5C6 = {12} -> R2C6 = {45} (step 7)
25b. Min R2C6 = 4 -> max R12C5 = 8, no 8,9
25c. 9 in N2 locked in R23C4, locked for C4 amd 21(3) cage -> no 9 in R3C3
25d. 9 in N8 locked in R78C6 = {69}(step 20d)
26. Naked pair {57} in R69C6, locked for C6 -> R2C6 = 4, R3C67 = [17], R5C6 = 2, R6C4 = 1, R6C1 = 2, R5C1 = 1, R9C34 = [13]
26a. Naked pair {69} in R78C6, locked for C6 and N8 -> R1C6 = 8
27. R45C6 = 5 -> R56C5 = 16 = {79}, locked for C5 and N5 -> R5C4 = 6, R6C6 = 5, R9C6 = 7, R9C7 = 6, R7C7 = 8, R7C3 = 9, R78C6 = [69], R6C3 = 7 (cage sum), R56C5= [79], R6C2 = 8, R4C2 = 9, R4C5 = 8, R3C5 = 3 (cage sum), R23C8 = [32]
28. Naked triple {579} in R123C4, locked for C4 and N2 -> R78C4 = [28], R78C9 = [12]
29. Naked pair {45} in R9C58, locked for R9 -> R9C12 = [82], R8C2 = 7 (cage sum)
30. Naked pair {45} in R8C38, locked for R8 -> R8C1 = 6, R8C5 = 1
31. R6C2 + R8C1 = 14 -> R7C12 = 8 = [35], R79C5 = [45], R89C8 = [54], R8C3 = 4, R5C23 = [43], R23C2 = [16] , R1C2 = 3, R12C7 = [15]
32. 21(3) cage at R2C4 = {579} (only remaining combination) -> R3C3 = 5, R3C4 = 9, R2C4 = 7
and the rest is naked singles
Happy Christmas to everyone on the forum!
This one felt a bit harder than last week so I'll rate it at 1.25.
Here is my walkthrough. It's late so I haven't had time to check it. I'll do that tomorrow, hope there aren't any mistakes apart from typos.
Edit. Went through again in the morning. I've simplified from step 24 onward. Step 24 had been written before I inserted step 20a. I haven't colour coded the changes this time, hope that's not a problem for anyone.
Prelims
a) R3C67 = {17/26/35}, no 4,8,9
b) R9C34 = {13}, locked for R9
c) R9C67 = {49/58/67}, no 2
d) R123C1 = {389/479/569/578}, no 1,2
e) 21(3) cage at R2C4 = {489/579/678}, no 1,2,3
f) R234C8 = {123}, locked for C8
g) R456C1 = 1{25/34}, 1 locked for C1 and N4
h) 19(3) cage in N6 = {289/379/469/478/568}, no 1
i) R789C5 = {127/145/235} (cannot be {136} which clashes with R9C4), no 6,8,9
1. 45 rule on C1234 1 innie R4C4 = 4
1a. R34C5 = 11 = {29/38/56}, no 1,7
2. 45 rule on C1 3 innies R789C1 = 17
2a. Cage overlap R67C2 = R9C1 + 5
2b. IOU no 5 in R6C2
3. 45 rule on C9 3 innies R789C9 = 12
3a. Cage overlap R67C8 = R9C9 + 4
3b. IOU no 4 in R6C8
4. 45 rule on C12 2 innies R15C2 = 7 = [16]/{25/34}, no 7,8,9, no 6 in R1C2
5. 45 rule on C89 2 innies R15C8 = 17 = {89}, locked for C8
5a. 4 in C5 locked in R789C5, locked for N9, clean-up: no 9 in R9C6
6. 18(3) cage in N9 = {459/468/567} (cannot be {289} because 2,8,9 only in R9C9), no 2
7. 45 rule on C6789 3 innies R245C6 = 9 = {126/135/234}, no 7,8,9
7a. Min R45C6 = 4 (from 21(4) cage) -> no 6 in R2C6
7b. Max R45C6 = 8 -> min R56C5 = 13, no 1,2,3
8. 45 rule on N3 3 outies R13C6 + R4C8 = 10, max R13C6 = 9, no 9 in R1C6
9. 45 rule on N1 2 outies R1C4 + R4C2 = 1 innie R3C3 + 9, min R3C3 = 4 -> min R1C4 + R4C2 = 13, no 1,2,3
10. 16(4) cage at R6C8 = {1267/1357/1456/2347/2356} (cannot be {1249/1258/1348} because R67C8 must contain two of 4,5,6,7), no 8,9
10a. 7 of {1267/1357/2347} must be in R6C8 -> no 7 in R78C9
10b. Cannot be {1456} because R7C8 = 4, R78C9 = {15/16} clash with 18(3) cage
10c. -> 16(4) cage at R6C8 = {1267/1357/2347/2356}
10d. -> R78C9 = {123}, no 5,6
11. R789C9 = 12 (step 3) = {129/138/237} (cannot be {147/156/246} because R78C9 only contain 1,2,3) -> R9C9 = {789}
11a. 18(3) cage in N9 (step 6) = {459/468/567}
11b. R9C9 = {789} -> no 7 in R89C8
12. 45 rule on N4 3 innies R4C2 + R6C23 = 24 = {789}, locked for N4
13. R67C2 = R9C1 + 5 (step 2a), min R67C2 = 8 -> no 2 in R9C1
13a. Max R9C1 = 9 -> max R67C2 = 14, no 7,8,9 in R7C2
14. 45 rule on R9 2 outies R8C28 = 1 innie R9C5 + 7, min R9C5 = 2 -> min R8C28 = 9, no 1,2 in R8C2
15. 45 rule on N6 3 innies R4C8 + R6C78 = 11 = [137/146/236/245/317/326] -> R6C7 = {1234}
15a. Max R6C7 = 4 -> min R6C6 + R7C7 = 13, no 1,2,3
16. Hidden triple {123} in N9 -> R8C7 = {123}
16a. Max R8C7 = 3 -> min R78C6 = 15, R78C6 = {6789}
17. 45 rule on R789 2 innies R7C37 = 2 outies R6C28 + 3, min R6C28 = 12 -> min R7C37 = 15, R7C37 = {6789}
17a. R7C37 = 15,16,17 -> R6C28 = 12,13,14 = [75/76/85/86/95], no 7 in R6C8
18. R7C8 = 7 (hidden single in C8), clean-up: no 6 in R9C6
18a. Naked triple {689} in R7C367, locked for R7
19. R789C9 (step 11) = {129/138}, 1 locked in R78C9 for C9 and N9
20. 1 in N6 locked in R4C8 + R6C7
20a. R4C8 + R6C78 (step 15) = [146] (only remaining permutation)
20b. R6C6 + R7C7 = 13 = [58/76]
20c. R78C9 = {12} (step 10c), locked for C9 and N9, R8C7 = 3, clean-up: no 5 in R3C6
20d. R78C6 = [69/87/96], no 8 in R8C6
21. Naked pair {23} in R23C8, locked for N3, clean-up: no 6 in R3C6
21a. Naked pair {45} in R89C8, locked for N9, R9C9 = 9 (step 11a), clean-up: no 4,8 in R9C6
21b. Naked pair {68} in R79C7, locked for C7, clean-up: no 2 in R3C6
22. Naked quad {5789} in R6C2356, locked for R6 -> R6C9 = 3
22a. 5 locked in R6C56 for N5, clean-up: no 6 in R3C5 (step 1a)
22b. R45C9 = 12 = {57} (only remaining combination), locked for C9 and N6
22c. Naked pair {29} in R45C7, locked for C7 and N6, R5C8 = 8, R1C8 = 9
23. 23(4) cage at R5C4, max R67C3 + R6C4 = 19 -> no 1,2,3 in R5C4
24. 45 rule on R123 1 remaining outie R4C2 = 1 innie R3C5 + 6 -> R3C5 = {23}, R4C2 = {89}, clean-up: no 2,3,6 in R4C5 (step 1)
24a. Naked pair {89} in R4C25, locked for R4 -> R45C7 = [29]
25. Hidden triple {123} in R45C6 + R6C4, no 6 in R45C6 -> R4C6 = 3, R4C1 = 5, R4C3 = 6, R45C9 = [75], clean-up: no 5 in R3C7
25a. R5C6 = {12} -> R2C6 = {45} (step 7)
25b. Min R2C6 = 4 -> max R12C5 = 8, no 8,9
25c. 9 in N2 locked in R23C4, locked for C4 amd 21(3) cage -> no 9 in R3C3
25d. 9 in N8 locked in R78C6 = {69}(step 20d)
26. Naked pair {57} in R69C6, locked for C6 -> R2C6 = 4, R3C67 = [17], R5C6 = 2, R6C4 = 1, R6C1 = 2, R5C1 = 1, R9C34 = [13]
26a. Naked pair {69} in R78C6, locked for C6 and N8 -> R1C6 = 8
27. R45C6 = 5 -> R56C5 = 16 = {79}, locked for C5 and N5 -> R5C4 = 6, R6C6 = 5, R9C6 = 7, R9C7 = 6, R7C7 = 8, R7C3 = 9, R78C6 = [69], R6C3 = 7 (cage sum), R56C5= [79], R6C2 = 8, R4C2 = 9, R4C5 = 8, R3C5 = 3 (cage sum), R23C8 = [32]
28. Naked triple {579} in R123C4, locked for C4 and N2 -> R78C4 = [28], R78C9 = [12]
29. Naked pair {45} in R9C58, locked for R9 -> R9C12 = [82], R8C2 = 7 (cage sum)
30. Naked pair {45} in R8C38, locked for R8 -> R8C1 = 6, R8C5 = 1
31. R6C2 + R8C1 = 14 -> R7C12 = 8 = [35], R79C5 = [45], R89C8 = [54], R8C3 = 4, R5C23 = [43], R23C2 = [16] , R1C2 = 3, R12C7 = [15]
32. 21(3) cage at R2C4 = {579} (only remaining combination) -> R3C3 = 5, R3C4 = 9, R2C4 = 7
and the rest is naked singles
Happy Christmas to everyone on the forum!