That's how far I've managed to get.CathyW wrote:I have 3 placements and am totally stuck.
I'm posting what I've done so far in the hope that someone will pick it up as a "tag" solving attempt. I get the impression from the posts by Afmob and Gary on the A85 thread that they have both got a bit further than I have.
Here are my opening steps. I'm using normal text because it's a separate thread and it's best for "tags".
Prelims
a) R1C34 = {79}, locked for R1
b) R12C5 = {14/23}
c) R1C67 = {38/56} (other combinations eliminated by step a)
d) R34C1 = {19/28/37/46}, no 5
e) R34C9 = {49/58/67}
f) R5C89 = {14/23}
g) R5C12 = {16/25} (cannot be {34} which clashes with R5C89)
h) R67C1 = {19/28/37/46}, no 5
i) R67C9 = {39/48/57}, no 1,2,6
j) R89C5 = {49/58/67}, no 1,2,3
k) R9C34 = {18/27/36/45}, no 9
l) R9C67 = {18/27/36/45}, no 9
m) 21(3) cage in N1 = {489/579/678}, no 1,2,3
n) 10(3) cage in N3 = {127/136/145/235}, no 8,9
o) 10(3) cage at R6C7 = {127/136/145/235}, no 8,9
p) 18(5) cage at R2C2 = {12348/12357/12456}, no 9
1. Killer pair 1,2 in R5C12 and R5C89, locked for R5
2. 21(3) cage in N1 = {489/678} (cannot be {579} because 7,9 only in R2C1), no 5, 8 locked for N1, clean-up: no 2 in R4C1
2a. 7,9 only in R2C1 -> R2C1 = {79}
2b. 8 locked in R1C12, locked for R1, clean-up: no 3 in R1C67
3. Naked pair {56} in R1C67, locked for R1, clean-up: no 7 in R2C1 (step 2) -> R2C1 = 9, R1C34 = [79], clean-up: no 1 in R34C1, no 3 in R4C1, no 1 in R67C1, no 2 in R9C4
3a. Naked pair {48} in R1C12, locked for R1 and N1, clean-up: no 1 in R2C5, no 6 in R4C1
4. 10(3) cage in N3 = {127/136/235} (cannot be {145} because 4,5 only in R2C9), no 4
4a. 5,6,7 only in R2C9 -> R2C9 = {567}
5. 45 rule on C1 3 outies R159C2 = 18 = {189/459/468} (cannot be {279/369/567} because R1C2 only contains 4,8, cannot be {378} because no 3,7,8 in R5C2), no 2,3,7, clean-up: no 5 in R5C1
5a. 1 of {189} must be in R5C2 -> no 1 in R9C2
5b. 5 of {459} must be in R5C2 -> no 5 in R9C2
5c. 6 of {468} must be in R5C2 -> no 6 in R9C2
6. 45 rule on C9 3 outies R159C8 = 12 = {129/138/147/237/246/345} (cannot be {156} because 5,6 only in R9C8)
6a. 5,6,7,8,9 only in R9C8 -> R9C8 = {56789}
7. 45 rule on C6789 4 innies R456C6 + R5C7 = 29
7a. Max R456C6 = 24 -> min R5C7 = 5
7b. Max R5C7 = 9 -> min R456C6 = 20, no 1,2
8. Killer triple 4,7,8 in R1C1, R4C1 and R67C1, locked for C1
9. 5 in C1 locked in R89C1, locked for N7, clean-up: no 4 in R9C4
9a. 15(3) cage in N7 = 5{19/28/46}, no 3
10. 45 rule on R9 3 outies R8C159 = 18 = {189/279/369/459/468/567} (cannot be {378} because no 3,7,8 in R8C1)
10a. 1,2 of {189/279} must be in R8C1 -> no 1,2 in R8C9
I've looked at the 5-cell cages and the outies from R12, R89, C12 and C89 but so far haven't found anything useful from them.
Let's see how much further we can get before we need to resort to chains or hypotheticals. From the ratings that Afmob posted, I expect we will need to use them later in this puzzle.