1. All diagonal cages of 2 with odd sum have one consecutive combination which cannot work with FNC
a. the three diagonal 9/2 <> {45}
b. 15/2 @ n3 <> {78} = {69} (NP @ n3, w:r234c678)
2a. 10/2 @ r23c6 = {28|37} = {2|3..} -> 5/2 @ r4c78 <> {23} = {14} (NP @ r4, w:r234c678, n6)
b. 9/2 @ r4c34 = {27|36}
3a1. Innies @ w:r678c678 -> r6c6+r7c7+r8c8 = 9
a2. <> {234} because it would violate the FNC rule (no possible cell to place the 3 without it being diagonally adjacent to a 2 or 4).
a3. -> {1(26|35)} = {5|6..} -> 1 locked for w:r678c678
b. 14/2 @ r6c78 = {59|68} = {5|6..}; KNP {56} with h9/3 @ w:r678c678
c. 9/2 @ n9 = {27} (NP @ n9, w:r678c678)
d. 13/2 @ r78c6 = {49} (NP @ n8, c6, w:r678c678)
e. 14/2 @ r6c78 = {68} (NP @ n6, r6, w:r678c678); FCN -> r57c6..9 <> 7
f. 9/2 @ n9: r7c8 = 2, r8c7 = 7
4a. 13/2 @ r6c34 = {49} (NP @ r6, w:r678c234)
b. 10/2 @ r78c4 = [82|73] = {2|7..} -> 9/2 @ n7 <> {27} = {18|36}
c. Since r8c4 = {23}, FNC -> r7c35,r9c5 <> {23} (Note: cannot remove {23} from r9c3 since it's a NOT a buddy/peer of r8c4)
d. Innies @ w:r678c234 -> r67c2+r8c3 = 13; 5 locked for w:r678c234 -> {5(17|26)}
e. FNC -> r7c2,r8c3 <> {56} -> r6c2 <> 2
5a. Innies @ w:r234c234 -> r2c3+r34c2 = 21 (no {123})
b. 2 @ c2 locked @ r1259c2; CPE -> r1c3 <> 2 (either in n1 or hw:r159c234)
c. 4 @ c2 locked @ r1359c2; CPE -> r1c3 <> 4
d. 6/2 @ r1 = {15} (NP @ r1, n1)
e. 9/2 @ n1 = {27|36}
f. two 9/2 @ w:r234c234 = NQ {2367} @ w:r234c234
g. 6/2 @ r23c4 = {15} (NP @ n2, c4, w:r234c234)
h. h21/3 @ r2c3+r34c2 = {489}
i. Since r4c2 = {89}; FNC -> r5c13 <> {89}
6a. h13/3 @ r67c2+r8c3 = {157|256}; FNC -> r7c2,r8c3 <> {56} -> r67c2 = {17|56|57} = {1|5..}
b. KNP {15} @ c2 with r1c2 -> r8c2 <> 1 = {38}
c. 9/2 @ n7 -> r7c3 = {16}
7a. h21/3 @ r2c3+r34c2 = {489}
b. Since r6c3 = {49} -> r2c3,r4c2 <> [49] -> r3c2 <> 8 = {49}, r2c3,r4c2 = {4|9..} (Note: one may prefer using ALS-XZ here)
c. r6c3 and r2c3,r4c2 = KNP {49} -> 4 locked @ r26c3 for c3
d. r269c3 = HT {489} @ c3 -> r9c3 = {89}
e. FNC -> r8c2 = 3, r7c3 = 6, r78c4 = [82], r6c34 = [49]
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