SudokuSolver Forum

3x3::k:6144:6144:6144:6144:5889:5889:3330:3330:3330:7427:7427:7427:6144:2308:5889:5889:6405:2566:7427:1799:1799:7432:2308:3337:6405:6405:2566:7427:4618:7432:7432:7432:3337:6405:3083:2566:4618:4618:4108:6413:7432:2062:1807:3083:3083:2064:2064:4108:6413:7432:2062:1807:6161:6161:3346:2064:4883:6413:6413:6413:6161:6161:2836:3346:4883:4883:6933:6413:4374:4374:2836:2836:6933:6933:6933:6933:4374:4374:4631:4631:4631:

1. 16/2@r5c3 = {79}
-> 18/3@r4c2 = {468}
-> Remaining cells in n4 are {1235}
-> r7c2 from (1245)

2. Innies - Outies n7 -> r89c4 = r7c2+14
Since r89c4 = Max +17
-> r7c2 = Max 3
-> r7c2 from (12)

3. {79} in r56c3 prevents 19/3@r7c3 from being {379}
-> 3 in n7 in r9c123
-> Innies n7 r7c2+r9c123 = +13 must include (13)
-> must be {1237} or {1345}

But putting a 2 in r7c2 puts r9c123 = {137} and there is no solution for 27/5@r8c4

-> r7c2 = 1
-> r6c12 = {25}
-> r4c13 = {13}

Also r9c123 = {237} or {345}
Also -> r89c4 = +15

4. Missing values from 25/6@r5c4 are a 20/3
Must include the two values at r89c4 which equal +15
-> third missing value is a 5 which must go in r8c6 or r9c56. (I.e., in the 17/4@r8c6)

5. Innies c789 -> r28c7 = +15
-> Min r8c7 = 6
-> Other two cells (to go with the 5 already there) in the 17/4@r8c6 sum to at most +6 and must both be <= 4.

6. (6789) in r9.
At most two of r9c789 are from (6789).
r9c56 are each at most 5
r9c4 from (6789)
-> At least one of (6789) must be in r9c123
-> r9c123 = {237}
-> r89c4 = {69}
-> 8 in r9c789

7. Outies n1 -> r12c4 + r4c1 = +15
r4c1 from (13)
-> r12c4 from +14 or +12
But {69} at r89c4 prevent r12c4 from being +14
-> r4c1 = 3
-> r4c3 = 1
-> r12c4 = +12
Also HS 1 in c1 -> r1c1 = 1

8. HS 1 in c4 -> 1 in r56c4
-> 1 in r8c6 or r9c56 in n8
-> 17/4@r8c6 = {15 (47|29)} with 7 or 9 in r8c7.
-> r56c4 = {12} or {14}
Also -> r2c7 from (68)

9. Since 1 in r56c4 and {25} in r6c12 -> 8/2@r5c6 from [26] or [53]
Missing values from 29/6@r3c4 are a 16/3.
Those missing values must include the 2 or 4 from r56c4
The other two missing values must go in r456c6 in n5

(a) {14} in r56c4 means the other two missing values are {57} or {39} -> 8/2@r5c6 = [53]
(b) {12} in r56c4 -> 8/2@r5c6 = [53]

Either way -> 8/2@r5c6 = [53]

10. 8/2@r5c6 = [53] -> r9c5 = 5
-> 1 in r89c6
-> HS 1 in c5 -> 9/2@r2c5 = {18}
-> Hidden Group 12/2@r12c4 = {57}

11. Innies - Outies n2 -> r3c4 + r3c6 = r2c7 + 1
-> (Since 1 already in n2) whatever goes in r2c7 cannot go in r3c4 or r3c6
-> must be from one of the values in r12c4 or r23c5. I.e., from (5718)
-> r2c7 = 8 (using Step 8)
-> r23c5 = [18]
Also -> r8c7 = 7
-> r89c6 = {14}
-> r56c4 = {14}
Also -> 13/2@r3c6 = [67]
-> r4c45 + r56c5 = {2689} = +25
-> r3c4 = 3
Also r1c5 = 4
-> r12c6 = {29}
-> NS r7c6 = 8
-> r4c4 = 8
-> r456c5 = {269}
Also -> NS r7c4 = 2
-> r78c5 = [73]
Also r7c78 = +9
-> r6c89 = +15

12. Innies n9 -> r7c78 = +9 -> No 9.
-> 9 in n9 can only be in r9
-> 18/3@r9c7 = {189}
-> r89c4 = [96]
-> r89c6 = [14]
-> Also HS 9 in n7 -> 13/2@r7c1 = [94]
-> 19/3@r7c3 = {568}

13. 1 in r1c1 and 3 in r3c4 -> 7/2@r3c2 = {25}
-> HS 5 in c1 -> r6c12 = [52]
-> 7/2@r3c2 = [52]
-> HS 2 in c1 r9c1 = 2
-> r9c23 = [73]
-> HS 3 in n1 -> r1c2 = 3
-> r1c3 = 8
-> r8c2 = 8 and r78c3 = {56}
-> r5c1 = 8 and r45c2 = {46}
Also 8 in n6 can only go in r6c89 -> r6c89 = {78}
-> 16/2@r5c3 = [79]
Also HS 9 in n1 -> r2c2 = 9
Also r2c3 = 4
Also r23c1 = [67]
Also r12c6 = [92]
-> 13/3@r1c7 can only be {256}
-> r12c4 = [75]

14. Remaining values in r2 and r3
-> r2c89 = {37} and r3c789 = {149}
-> 10/3@r2c9 can only be [712] or [316]
But the former would put two 9s in 25/4@r2c8
-> 10/3@r2c9 = [316]
-> 25/4@r2c8 = [7{49}5]
-> 7/2@r5c7 = [34]
-> r3c78 = [94]

Rest is clean up

Thanks Ed for pointing out corrections and suggesting clarifications.

Prelims

a) R23C5 = {18/27/36/45}, no 9
b) R3C23 = {16/25/34}, no 7,8,9
c) R34C6 = {49/58/67}, no 1,2,3
d) R56C3 = {79}
e) R56C6 = {17/26/35}, no 4,8,9
f) R56C7 = {16/25/34}, no 7,8,9
g) R78C1 = {49/58/67}, no 1,2,3
h) 10(3) cage at R2C9 = {127/136/145/235}, no 8,9
i) 8(3) cage at R6C1 = {125/134}
j) 19(3) cage at R7C3 = {289/379/469/478/568}, no 1
k) 11(3) cage at R7C9 = {128/137/146/236/245}, no 9

1. Naked pair {79} in R56C3, locked for C3 and N4
1a. 18(3) cage at R6C1 = {468} (only remaining combination), locked for N4
1b. 19(3) cage at R7C3 = {289/469/478/568} (cannot be {379} because 7,9 only in R8C2), no 3
1c. 7,9 of {289/469/478} must be in R8C2 -> no 2,4 in R8C2

2. 45 rule on R1 2 innies R1C56 = 1 outie R2C4 + 8, IOU no 8 in R1C56
2a. Max R1C56 = 16 -> max R2C4 = 8

3. 45 rule on R9 2 innies R9C56 = 1 outie R8C4
3a. Max R9C56 = 9, no 9 in R9C56
3b. Min R9C56 = 3 -> min R8C4 = 3

4. 45 rule on N7 2 outies R89C4 = 1 innie R7C2 + 14
4a. Max R89C4 = 17 -> max R7C2 = 3
4b. 8(3) cage at R6C1 = {125} (only remaining combination), 5 locked for R6 and N4, clean-up: no 3 in R5C6, no 2 in R5C7
4c. R7C2 = {12} -> R89C4 = 15,16 = {69/78/79}, no 1,2,3,4,5
4d. 3 in N4 only in R4C13, locked for R4
[Ed pointed out that there was also 3 in R4C13, CPE no 3 in R2C3; I usually spot this type of CPE. I spotted it later in step 9e.]

5. 45 rule on N1 3(2+1) outies R12C4 + R4C1 = 15
5a. Max R4C1 = 3 -> min R12C4 = 12, no 1,2,3 in R1C4, no 1,2 in R2C4

6. 45 rule on N1 3 innies R1C123 = 1 outie R4C1 + 9
6a. Max R4C1 = 3 -> max R1C123 = 12
6b. 45 rule on R1 6 innies R1C123456 = 32, max R1C123 = 12 -> min R1C456 = 20, no 1,2 in R1C456

7. 45 rule on N6 4 innies R4C79 + R4C89 = 26 = {2789/3689/4589/4679/5678}, no 1

8. 25(6) cage at R5C4 = {123469/123478/123568} (cannot be {124567} which clashes with R89C4, step 4c)

9. 3 in N7 only in R9C123, locked for R9
9a. R7C2 = {12} -> R89C4 = {69/78/79} (step 4c)
9b. 45 rule on N7 4 innies R7C2 + R9C123 = 13 and contains 3 = {1237/1345}, no 6,8,9
9c. 1 of {1237/1345} must be in R7C2 (R7C2 + R9C123 = 2{137} clashes with R89C4 = {79} -> R7C2 = 1, R6C12 = {25}, locked for R6 and N4, clean-up: no 6 in R3C3, no 6 in R5C6, no 5 in R5C7
9d. Naked pair {13} in R4C13, locked for R4
9e. R4C13 = {13}, CPE no 1,3 in R2C3
9f. 19(3) cage at R7C3 (step 1b) = {289/469/568} (cannot be{478} which clashes with R9C123), no 7

10. R56C7 = {16/34}
10a. 12(3) cage at R4C8 = {129/156/237/345}(cannot be {138/147/246} which clash with R56C7), no 8
10b. Killer pair 1,3 in 12(3) cage and R56C7, locked for N6

11. 45 rule on C789 2 innies R28C7 = 15 = {69/78}
11a. Min R8C7 = 6 -> max R8C6 + R9C56 = 11, no 9 in R8C6

12. 45 rule on N9 2 outies R6C89 = 1 innie R8C7 + 8
12a. Min R8C7 = 6 -> min R6C89 = 14, no 4 in R6C89

13. 45 rule on C123 4 outies R1289C4 = 1 innie R4C3 + 26
13a. R4C3 = {13} -> R1289C4 = 27,29 must contain 9, locked for C4

14. 45 rule on N78 3(2+1) outies R56C4 + R8C7 = 12
14a. Min R8C7 = 6 -> max R56C4 = 6, no 6,7,8 in R56C4

15. 45 rule on N7 2 outies R89C4 = 15 = {69/78}
15a. 25(6) cage at R5C4 (step 8) = {123469/123478} (cannot be {123568} which clashes with R89C4), no 5
15b. 25(6) cage = {123469/123478}, CPE no 1 in R56C5
15c. Killer quad 6,7,8,9 in 25(6) cage and R89C4, locked for N8

16. R9C123 (steps 9b and 9c) = {237/345} = 12
16a. 45 rule on R9 3 remaining innies R9C456 = 15 = {159/456} (cannot be {249/258} which clash with R9C123, cannot be {168/267} because 6,7,8 only in R9C4), no 2,7,8, 5 locked for R9 and N8, clean-up: no 7,8 in R8C4 (step 15)
16b. Naked pair {69} in R89C4, locked for C4 and N8

17. 8 in R9 only in R9C789, locked for N9, clean-up: no 7 in R2C7 (step 11)
17a. Hidden killer pair 6,9 in R9C4 and 18(3) cage at R9C7 for R9, R9C4 = {69} -> 18(3) cage must contain one of 6,9 -> 18(3) cage = {189/468}, no 2,7
17b. Killer pair 1,4 in R9C56 and 18(3) cage, locked for R9

18. Naked triple {237} in R9C123, locked for N7, clean-up: no 6 in R78C1

19. R12C4 + R4C1 = 15 (step 5)
19a. R12C4 cannot total 14 -> R12C4 = 12 = {48/57}, R4C1 = 3, R4C3 = 1, clean-up: no 6 in R3C2
19b. R23C5 = {18/27/36} (cannot be {45} which clashes with R12C4), no 4,5 in R23C5

20. 1 in C4 only in R56C4, locked for N5 and 25(6) cage at R5C4, no 1 in R8C5, clean-up: no 7 in R56C6

21. R4C1 = 3 -> 29(4) cage at R2C1 = {23789/34679/35678} (cannot be {34589} which clashes with R3C23), no 1

22. R1C123 = R4C1 + 9 (step 6), R4C1 = 3, R1C1 = 1 (hidden single in C1) -> R1C23 = 11 = {38/56}/[92] (cannot be [74] which clashes with 29(4) cage at R2C1, no 2,4,7 in R1C2, no 4 in R1C3
22a. 13(3) cage at R1C7 = {238/247/256/346}, no 9

23. 1,5 in N8 only in 17(4) cage at R8C6 = {1259/1457}, no 3,6, clean-up: no 9 in R2C7 (step 11)
23a. 3 in N8 only in R7C456 + R8C5, locked for 25(6) cage at R5C4, no 3 in R56C4
23b. 9 in N3 only in R2C8 + R3C78, locked for 25(4) cage at R2C8, no 9 in R4C7

24. 45 rule on N3 2 outies R4C79 = 1 innie R2C7 + 3
24a. R2C7 = {68} -> R4C79 = 9,11 = {27/47/56} (cannot be {45} because R2C7 + R4C79 = 6{45} clashes with R56C7 = {34}), no 8 in R4C7

25. 8 in N6 only in R6C89, locked for R6
25a. R6C89 = R8C7 + 8 (step 12)
25b. R8C7 = {79} -> R6C89 = {78/89}, no 6
25c. Naked triple {789} in R6C3 and R6C89, locked for R6

26. 45 rule on N9 3 innies R7C78 + R8C7 = 16 = {259/349/367/457}
26a. R8C7 = {79} -> no 7,9 in R7C78

27. R7C1 = 9 (hidden single in R7), R8C1 = 4
27a. 4 in N4 only in R45C2, locked for C2, clean-up: no 3 in R3C3

28. 29(5) cage at R2C1 = {23789/34679/35678}
28a. 9 of {23789} must be in R2C2 -> no 2 in R2C2
28b. 6 or 8 of {35678} must be in R3C1 (otherwise R2C123 clashes with R2C7) -> no 5 in R3C1

29. Hidden killer triple 7,8,9 in 29(6) cage at R3C4 and R4C6 for N5, 29(6) cage cannot contain all of 7,8,9 -> 29(6) cage must contain two of 7,8,9 in N5 (no 7,8 in R3C4) and R4C6 = {789}, R3C6 = {456}

30. 9 in N2 only in 23(4) cage at R1C5 = {1589/1679/2489/3569} (cannot be {2579/3479} because R2C7 only contains 6,8)
30a. R2C7 = {68} -> no 6,8 in R1C56 + R2C6
30b. R1C123 = 12 (step 22), 13(3) cage at R1C7 -> R1C456 = 20 = {389/479} (cannot be {578} because 23(4) cage doesn’t contain both of 5,7), no 5, 9 locked for R1 and N2, clean-up: no 2 in R1C3 (step 22), no 7 in R2C4 (step 19a)
[Finally cracked by steps 29 and 30; the rest is fairly straightforward.]

31. R2C2 = 9 (hidden single in N1)
31a. 29(5) cage at R2C1 (step 28) = {23789/34679}, 7 locked for C1 -> R9C123 = [273], R6C12 = [52], clean-up: no 8 in R1C2 (step 22), no 5 in R3C3
31b. 29(5) cage = {23789/34679} -> R2C3 = {24}

32. 23(4) cage at R1C5 (step 30) = {1679/2489/3569} (cannot be {1589} because 1,5 only in R2C6)
32a. 1,2,5 only in R2C6 -> R2C6 = {125}

33. Naked triple {125} in R258C6, locked for C6 -> R9C6 = 4, R3C6 = 6, R4C6 = 7, R6C6 = 3, R5C6 = 5, R9C5 = 5 (hidden single in R9), clean-up: no 4 in R5C7
33a. R9C56 = [54] = 9 -> R8C67 = 8 = [17], R2C7 = 8 (step 11), R12C6 = [92], R1C5 = 4 (cage sum), R2C3 = 4, R3C3 = 2, R3C2 = 5, R2C4 = 5, R1C4 = 7 (step 19a), R3C4 = 3, R23C5 = [18]

34. 13(3) cage at R1C7 = {256} (only remaining combination), locked for R1 and N3 -> R1C23 = [38]

35. R4C79 = R2C7 + 3 (step 24)
35a. R2C7 = 8 -> R4C79 = 11 = {56}, locked for R4 and N6, clean-up: no 1 in R56C7
35b. R56C7 = [34]

36. R6C5 = 6, R45C5 = {29}, locked for C5 and N5 -> R56C4 = [41]

37. 10(3) cage at R2C9 = {136} (only remaining combination, cannot be {145} because 1,4 only in R3C9) = [316]

38. Naked pair {25} in R18C9, locked for C9 -> R7C9 = 4, R8C89 = 7 = {25}, locked for R8 and N9

39. 12(3) cage at R4C8 = {129} (only remaining combination) -> R5C9 = 9, R45C8 = [21]

and the rest is naked singles.

I'll rate my walkthrough for A271 at Hard 1.25; after step 9c I never used anything harder than combination analysis and hidden killer pairs/triples. I can only think that the reason why the SS score is so much higher is that it isn't programmed to make our first breakthrough, my step 9c and the middle part of wellbeback's step 3.

Preliminaries courtesy of SudokuSolver
Cage 16(2) n4 - cells ={79}
Cage 7(2) n1 - cells do not use 789
Cage 7(2) n6 - cells do not use 789
Cage 8(2) n5 - cells do not use 489
Cage 13(2) n7 - cells do not use 123
Cage 13(2) n25 - cells do not use 123
Cage 9(2) n2 - cells do not use 9
Cage 8(3) n47 - cells do not use 6789
Cage 10(3) n36 - cells do not use 89
Cage 11(3) n9 - cells do not use 9
Cage 19(3) n7 - cells do not use 1

1. 16(2)n4 = {79}: both locked for n4 and c3
1a. 19(3)n7 cannot have both 7 & 9 -> no 3

2. 18(3)n4 = {468} only combination: all locked for n4

3. "45" on n7: 2 outies r89c4 - 14 = 1 innie r7c2
3a. max. r89c4 = 17 -> max. r7c2 = 3
3b. min. r89c4 = 15 (no 1,2,3,4,5)

4. 8(3)r6c1 = {125} only combination
4a. 5 only in r6c12: 5 locked for r6 and n4
4b. no 3 in r5c6
4c. no 2 in r5c7

5. "45" on n9: 1 innie r8c7 + 8 = 2 outies r6c89: but r6c89 cannot be {79} = 16 because of r6c3 -> no 8 in r8c7

6. "45" on c789: 2 innies r28c7 = 15 = {69}[87]

7. r56c4 + r8c7 between them see all of n8 -> cannot have repeats (no eliminations yet)
7a. "45" on n78: 1 innie r7c2 + 11 = 3 outies r56c4 + r8c7
7b. r7c2 = (12) -> 3 outies = 12 or 13 but can't be {16}[6] since can't have repeats -> max r56c4 = 7 = {25}(no 6789)

8. "45" on n7: 2 outies r89c4 - 14 = 1 innie r7c2
8a. r7c2 = (12) -> r89c4 = 15 or 16 = {69/78/79} = [6/7..]
8b. 25(6)r5c4: {124567} blocked by r89c4
8c. = {123469/123478/123568}
8d. Must have two of 6,7,8,9 which are only in n8
8e. -> Killer quad 6,7,8,9 with r89c4: all locked for n8

9. 3 in n7 only in r9: 3 locked for r9

10. "45" on r9: 3 outies r8c467 = 17
10a. min. r8c47 = 13 -> max. r8c6 = 4
10b. = {179/269/278/368/467} ie, can't have both 3 & 9

11. 17(4)r8c7: {1349} blocked by can't have both 3 & 9 in r8c67
11a. {1367} blocked by 6 & 7 only in r8c7
11b. = {1259/1457/2357/2456}
11c. must have 5: 5 locked for n8 and r9

12. 19(3)n7: {478} blocked by 13(2)n7 = [4/7/8]
12a. = {289/469/568} = [2/6..]

13. 27(5)r8c4 = {13689/23679}
13a. from step 8a. r89c4 = {69/78/79}
13b. but {78} blocked by 27(5)r8c4 can't have both 7 & 8
13c. but {79} blocked by {236} in n7 clashes with 19(3)(step 12) [Andrew saw this as blocked by 2 in r7c2 from IODn7 = -14]
13d. -> r89c4 = {69} only: both locked for c4 and n8 and 27(5)
13e. no 6,9 in r9c123
13f. r89c4 = 15 -> r7c2 = 1 (IODn7 = -14)
13g. r6c12 = {25} only: 2 locked for n4 and r6
13h. no 6 in r5c6, no 5 in r5c7
13i. no 6 in r3c3

14. "45" on n1: 3 outies r12c4 + r4c1 = 15
14a. but r12c4 cannot sum to 14 -> no 1 in r4c1
14b. r4c13 = [31]
14c. -> r12c4 = 12 = {48/57}(no 1,2,3)
14d. no 6 in r3c2

15. 1 in c4 only in r56c4: 1 locked for n5 and 25(6)r5c4
15a. no 1 in r8c5
15b. no 7 in 8(2)n5

16. 1 in n8 only in 17(4)r8c6 = {1259/1457}(no 3,6)
16a. no 9 in r2c7 (h15(2)r28c7)

17. "45" on n78: 3 outies r56c4 + r8c7 = 12 and must have 1 in r56c4.
17a. r8c7 = (79) -> r56c4 = 3 or 5 = [21]/{14}(no 3,5) = [2/4..]

18. 29(6)r3c4 cannot have three of {789} -> r4c6 must have one of 7,8,9 for n5 (Hidden killer triple)
18a. no 7,8,9 in r3c6 [Andrew noticed that step 18. also means no 7,8 in r3c4. Didn't need that or see that for this WT but always enjoy finding them]

19. 29(6)r3c4 = {123689/124589/124679/125678/134579/134678}
19a. but {124589/124679} blocked by r56c4 = [2/4](step 17a)
19b. = 29(6)r3c4 = {123689/125678/134579/134678}

Wellbeback's step 9 does this next step a different and very interesting way.
20. n5 must have 4 in r56c4 or [21][53] in r56c4+r56c6
20a. 29(6)r3c4: [1]{34579} blocked since it sees all 4 in r56c4 and has at least one of 3 or 5 in n5 which clashes with r56c6
20b. 29(6) = {123689/125678/134678}(note: must have one of 3 or 5)
20c. 29(6) must have 6 which is only in c5: 6 locked for n5 & c5
20d. no 3 in 9(2)n5

21. 8(2)n5 = [53]
21a. 29(6) must have 3 or 5 which are only in r3c4 -> r3c4 = (35)
21b. no 4 in r5c7
21c. no 8 in r4c6

Missing routine clean-up from here
22. Hidden single 5 in n8 -> r9c5 = 5

23. "45" on c6789: 1 remaining outie r1c5 + 4 = 1 innie r7c6 = [37/48]

24. 1 in c5 only in 9(2)n2 = {18} only: both locked for n2 & 8 for c5

25. h12(2)r12c4 = {57} only: both locked for n2, c4 and 24(5)r1c1
25a. r3c4 = 3, r1c5 = 4 -> r7c6 = 8 (step 23), r34c6 = [67]

26. r12c6 = {29} = 11 -> r2c7 = 8 (cage sum) -> r8c7 = 7 (h15(2)r28c7) -> r56c4 = 5 = {14} only (step 17a): 4 locked for c4, r47c4 = [82], r78c5 = [73], r23c5 = [18]

27. 7(2)n1 = {25} only combination: both locked for n1 and r3

28. 24(5)r1c1 = {13578} only combination: r1c1 = 1, r1c23 = {38} only: 3 locked for r1

29. 13(3)n3 = {256} only combination, all locked for n3 and 2 for r1, r12c4 = [75], r12c6 = [92]

30. 25(4)r2c8 = {3679/4579}(no 1,2)
30a. must have 5 or 6 which are only in r4c7 -> r4c7 = (56)

31. "45" on n3: 2 outies r4c79 = 11 = {56} only: both locked for n6 & 6 for r4

32. 7(2)n6 = [34] only permutation, r3c7 = 9, r4c2 = 4, r56c6 = [41]

33. Hidden single 1 in c7 -> r9c7 = 1
33a. r9c89 = 17 (cage sum) = {89} only: both locked for r9 and n9

34. Hidden single 1 in n3 -> r3c9 = 1
34a. -> r24c9 = 9 (cage sum) = [36/45]

35. 7 in n3 only in c8: locked for c8

36. 12(3)n6 = {129} only combination: locked for n6
36a. r5c8 = 1, r6c89 = [87], r9c89 = [98], r4c58 = [92], r89c4 = [96]

37. Hidden single 2 in n9 -> r8c9 = 2

38. Naked pair {56} in r14c9: both locked for c9

39. Hidden single 9 in n7 -> r7c1 = 9

A few cage sums and singles left