6
1
2
4
7
8
1
4
7
1
6
8
1
9
9
4
6
4
8
5
9
5
6
7
8

This Sudoku Puzzle has 72 steps and it is solved using Naked Single, Full House, Hidden Single, Locked Candidates Type 1 (Pointing), Uniqueness Test 4, Hidden Rectangle, Discontinuous Nice Loop, Locked Candidates Type 2 (Claiming), Naked Triple, undefined, Empty Rectangle, Jellyfish techniques.

Try To Solve This Puzzle

## Solution Steps:

1. Row 1 / Column 6 → 3 (Naked Single)
2. Row 3 / Column 6 → 8 (Naked Single)
3. Row 2 / Column 6 → 1 (Naked Single)
4. Row 2 / Column 5 → 5 (Naked Single)
5. Row 3 / Column 4 → 9 (Naked Single)
6. Row 1 / Column 4 → 6 (Full House)
7. Row 6 / Column 5 → 3 (Naked Single)
8. Row 4 / Column 5 → 4 (Naked Single)
9. Row 8 / Column 5 → 1 (Full House)
10. Row 6 / Column 9 → 7 (Hidden Single)
11. Row 7 / Column 6 → 4 (Hidden Single)
12. Row 9 / Column 7 → 4 (Hidden Single)
13. Row 7 / Column 4 → 8 (Hidden Single)
14. Row 1 / Column 1 → 4 (Hidden Single)
15. Row 5 / Column 3 → 4 (Hidden Single)
16. Row 4 / Column 9 → 8 (Hidden Single)
17. Row 4 / Column 7 → 1 (Hidden Single)
18. Locked Candidates Type 1 (Pointing): 5 in b1 => r56c2<>5
19. Locked Candidates Type 1 (Pointing): 7 in b7 => r8c4<>7
20. Uniqueness Test 4: 2/7 in r5c46,r9c46 => r59c4<>2
21. Hidden Rectangle: 2/8 in r2c23,r6c23 => r2c2<>2
22. Discontinuous Nice Loop: 9 r2c2 -9- r1c3 -7- r1c8 =7= r2c8 =6= r5c8 -6- r5c2 =6= r6c2 =8= r2c2 => r2c2<>9
23. Discontinuous Nice Loop: 3 r7c2 -3- r7c1 -2- r6c1 -5- r6c7 =5= r3c7 -5- r3c2 =5= r1c2 =9= r9c2 =1= r7c2 => r7c2<>3
24. Hidden Rectangle: 1/2 in r7c28,r9c28 => r9c8<>2
25. Discontinuous Nice Loop: 9 r8c1 -9- r4c1 =9= r4c3 -9- r1c3 -7- r8c3 =7= r8c1 => r8c1<>9
26. Discontinuous Nice Loop: 1/2/3 r9c2 =9= r1c2 =5= r1c8 -5- r3c7 =5= r6c7 -5- r6c1 =5= r4c1 =9= r4c3 -9- r8c3 =9= r9c2 => r9c2<>1, r9c2<>2, r9c2<>3
27. Row 9 / Column 2 → 9 (Naked Single)
28. Row 1 / Column 2 → 5 (Naked Single)
29. Row 9 / Column 8 → 1 (Hidden Single)
30. Row 7 / Column 2 → 1 (Hidden Single)
31. Row 8 / Column 9 → 9 (Hidden Single)
32. Row 8 / Column 7 → 6 (Hidden Single)
33. Row 6 / Column 2 → 6 (Hidden Single)
34. Row 6 / Column 3 → 8 (Hidden Single)
35. Row 2 / Column 2 → 8 (Hidden Single)
36. Locked Candidates Type 2 (Claiming): 3 in c7 => r2c89,r3c8<>3
37. Naked Triple: 2,3,5 in r23c7,r3c8 => r2c89<>2
38. Row 2 / Column 9 → 6 (Naked Single)
39. Row 5 / Column 8 → 6 (Hidden Single)
40. 2-String Kite: 2 in r3c2,r6c7 (connected by r5c2,r6c1) => r3c7<>2
41. Empty Rectangle: 2 in b7 (r48c4) => r4c1<>2
42. W-Wing: 3/2 in r2c7,r7c1 connected by 2 in r6c17 => r2c1<>3
43. W-Wing: 2/5 in r4c4,r6c7 connected by 5 in r5c49 => r4c8<>2
44. Jellyfish: 2 r2468 c1347 => r7c1<>2
45. Row 7 / Column 1 → 3 (Naked Single)
46. Row 4 / Column 8 → 3 (Hidden Single)
47. Row 9 / Column 9 → 3 (Hidden Single)
48. Row 9 / Column 4 → 7 (Naked Single)
49. Row 9 / Column 6 → 2 (Full House)
50. Row 5 / Column 6 → 7 (Full House)
51. Row 8 / Column 4 → 3 (Full House)
52. Row 5 / Column 4 → 5 (Naked Single)
53. Row 4 / Column 4 → 2 (Full House)
54. Row 5 / Column 9 → 2 (Naked Single)
55. Row 5 / Column 2 → 3 (Full House)
56. Row 6 / Column 7 → 5 (Full House)
57. Row 7 / Column 9 → 5 (Full House)
58. Row 3 / Column 2 → 2 (Full House)
59. Row 6 / Column 1 → 2 (Full House)
60. Row 7 / Column 8 → 2 (Full House)
61. Row 4 / Column 3 → 9 (Naked Single)
62. Row 4 / Column 1 → 5 (Full House)
63. Row 3 / Column 7 → 3 (Naked Single)
64. Row 3 / Column 8 → 5 (Full House)
65. Row 2 / Column 7 → 2 (Full House)
66. Row 8 / Column 1 → 7 (Naked Single)
67. Row 2 / Column 1 → 9 (Full House)
68. Row 8 / Column 3 → 2 (Full House)
69. Row 1 / Column 3 → 7 (Naked Single)
70. Row 1 / Column 8 → 9 (Full House)
71. Row 2 / Column 8 → 7 (Full House)
72. Row 2 / Column 3 → 3 (Full House)
The text passage describes a Sudoku puzzle and provides a detailed step-by-step solution, including the techniques used to solve each step.
no_question

the passage does not contain any mathematical questions or problems that require solving. it is purely a description of the solution steps for a sudoku puzzle.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
6
1
2
4
7
8
1
4
7
1
6
8
1
9
9
4
6
4
8
5
9
5
6
7
8

This Sudoku Puzzle has 72 steps and it is solved using Naked Single, Full House, Hidden Single, Locked Candidates Type 1 (Pointing), Uniqueness Test 4, Hidden Rectangle, Discontinuous Nice Loop, Locked Candidates Type 2 (Claiming), Naked Triple, undefined, Empty Rectangle, Jellyfish techniques.

Try To Solve This Puzzle

## Solution Steps:

1. Row 1 / Column 6 → 3 (Naked Single)
2. Row 3 / Column 6 → 8 (Naked Single)
3. Row 2 / Column 6 → 1 (Naked Single)
4. Row 2 / Column 5 → 5 (Naked Single)
5. Row 3 / Column 4 → 9 (Naked Single)
6. Row 1 / Column 4 → 6 (Full House)
7. Row 6 / Column 5 → 3 (Naked Single)
8. Row 4 / Column 5 → 4 (Naked Single)
9. Row 8 / Column 5 → 1 (Full House)
10. Row 6 / Column 9 → 7 (Hidden Single)
11. Row 7 / Column 6 → 4 (Hidden Single)
12. Row 9 / Column 7 → 4 (Hidden Single)
13. Row 7 / Column 4 → 8 (Hidden Single)
14. Row 1 / Column 1 → 4 (Hidden Single)
15. Row 5 / Column 3 → 4 (Hidden Single)
16. Row 4 / Column 9 → 8 (Hidden Single)
17. Row 4 / Column 7 → 1 (Hidden Single)
18. Locked Candidates Type 1 (Pointing): 5 in b1 => r56c2<>5
19. Locked Candidates Type 1 (Pointing): 7 in b7 => r8c4<>7
20. Uniqueness Test 4: 2/7 in r5c46,r9c46 => r59c4<>2
21. Hidden Rectangle: 2/8 in r2c23,r6c23 => r2c2<>2
22. Discontinuous Nice Loop: 9 r2c2 -9- r1c3 -7- r1c8 =7= r2c8 =6= r5c8 -6- r5c2 =6= r6c2 =8= r2c2 => r2c2<>9
23. Discontinuous Nice Loop: 3 r7c2 -3- r7c1 -2- r6c1 -5- r6c7 =5= r3c7 -5- r3c2 =5= r1c2 =9= r9c2 =1= r7c2 => r7c2<>3
24. Hidden Rectangle: 1/2 in r7c28,r9c28 => r9c8<>2
25. Discontinuous Nice Loop: 9 r8c1 -9- r4c1 =9= r4c3 -9- r1c3 -7- r8c3 =7= r8c1 => r8c1<>9
26. Discontinuous Nice Loop: 1/2/3 r9c2 =9= r1c2 =5= r1c8 -5- r3c7 =5= r6c7 -5- r6c1 =5= r4c1 =9= r4c3 -9- r8c3 =9= r9c2 => r9c2<>1, r9c2<>2, r9c2<>3
27. Row 9 / Column 2 → 9 (Naked Single)
28. Row 1 / Column 2 → 5 (Naked Single)
29. Row 9 / Column 8 → 1 (Hidden Single)
30. Row 7 / Column 2 → 1 (Hidden Single)
31. Row 8 / Column 9 → 9 (Hidden Single)
32. Row 8 / Column 7 → 6 (Hidden Single)
33. Row 6 / Column 2 → 6 (Hidden Single)
34. Row 6 / Column 3 → 8 (Hidden Single)
35. Row 2 / Column 2 → 8 (Hidden Single)
36. Locked Candidates Type 2 (Claiming): 3 in c7 => r2c89,r3c8<>3
37. Naked Triple: 2,3,5 in r23c7,r3c8 => r2c89<>2
38. Row 2 / Column 9 → 6 (Naked Single)
39. Row 5 / Column 8 → 6 (Hidden Single)
40. 2-String Kite: 2 in r3c2,r6c7 (connected by r5c2,r6c1) => r3c7<>2
41. Empty Rectangle: 2 in b7 (r48c4) => r4c1<>2
42. W-Wing: 3/2 in r2c7,r7c1 connected by 2 in r6c17 => r2c1<>3
43. W-Wing: 2/5 in r4c4,r6c7 connected by 5 in r5c49 => r4c8<>2
44. Jellyfish: 2 r2468 c1347 => r7c1<>2
45. Row 7 / Column 1 → 3 (Naked Single)
46. Row 4 / Column 8 → 3 (Hidden Single)
47. Row 9 / Column 9 → 3 (Hidden Single)
48. Row 9 / Column 4 → 7 (Naked Single)
49. Row 9 / Column 6 → 2 (Full House)
50. Row 5 / Column 6 → 7 (Full House)
51. Row 8 / Column 4 → 3 (Full House)
52. Row 5 / Column 4 → 5 (Naked Single)
53. Row 4 / Column 4 → 2 (Full House)
54. Row 5 / Column 9 → 2 (Naked Single)
55. Row 5 / Column 2 → 3 (Full House)
56. Row 6 / Column 7 → 5 (Full House)
57. Row 7 / Column 9 → 5 (Full House)
58. Row 3 / Column 2 → 2 (Full House)
59. Row 6 / Column 1 → 2 (Full House)
60. Row 7 / Column 8 → 2 (Full House)
61. Row 4 / Column 3 → 9 (Naked Single)
62. Row 4 / Column 1 → 5 (Full House)
63. Row 3 / Column 7 → 3 (Naked Single)
64. Row 3 / Column 8 → 5 (Full House)
65. Row 2 / Column 7 → 2 (Full House)
66. Row 8 / Column 1 → 7 (Naked Single)
67. Row 2 / Column 1 → 9 (Full House)
68. Row 8 / Column 3 → 2 (Full House)
69. Row 1 / Column 3 → 7 (Naked Single)
70. Row 1 / Column 8 → 9 (Full House)
71. Row 2 / Column 8 → 7 (Full House)
72. Row 2 / Column 3 → 3 (Full House)
user
The text passage describes a Sudoku puzzle and provides a detailed step-by-step solution, including the techniques used to solve each step.

TYPE: NO_QUESTION

The passage does not contain any mathematical questions or problems that require solving. It is purely a description of the solution steps for a Sudoku puzzle.