Sunday 24 July 2011

Locked Puzzle 4 (from Toronto Star)


Sunday’s Sudoku puzzle from Toronto Star (July 24, 2011) is an intimidating example of a locked puzzle. It is locked from the beginning and it is locked three times. The keys to unlocking it are in the full house and confinement techniques of elimination. Here is the puzzle and its annotated step-by-step solution.


For more information on SP Notation: First article – Sudoku Puzzle Notation and Elimination techniques
Toronto Star, July 24, 2011
Page IN2
Level: Hard

003009000
020004000
504230009
300000000
080701060
000000001
400012605
000600080
000500700



There are no fill steps from the start. The first key to unlock the puzzle is in the full house on cells D1 and D2.

1 and 8 are the only candidates in D1 and D2 because the top-center block and the D column have the other numbers: 2, 3, 4, 5, 6, 7 and 9.

Either (D1=1 and D2=8) or (D1=8 and D2=1). In either case, we can eliminate 8 as a candidate from all the other cells in the top-center block and in column D.

We begin with the elimination of 8 from the top-center block in cells E1, E2 and F3. The elimination of 8 from F3 leaves row 3 with only a cell for 8: cell G3.

1    D12 : 18 N
2    E1 / 8 B
3    E2 / 8 B
4    F3 / 8 B
5    G3 = 8 R

Only one more fill step can be done after:

6    I4 = 8 BC

The puzzle is locked again and we can continue with the elimination of 8 from column D (as a result of the full house in D1 and D2 for 1 and 8).

7    D6 / 8 C
8    D7 / 8 C

This leaves C7 as the only cell for 8 in row 7. Consequently, B7 is the only cell for 7 in row 7.
9    C7 = 8 R
10   B7 = 7 R




A
B
C
D
E
F
G
H
I
1


3


9



2

2



4



3
5

4
2
3



9
4
3








5

8

7

1

6

6








1
7
4



1
2
6

5
8



6



8

9



5


7










A
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C
D
E
F
G
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I
1


3
18  
8
9



2

2

18
8  
4



3
5

4
2
3
8  


9
4
3


8  





5

8

7

1

6

6



8  




1
7
4


8  
1
2
6

5
8



6



8

9



5


7











A
B
C
D
E
F
G
H
I
1
8  

3
18  

9



2
8  
2
8  
18  

4



3
5

4
2
3

8

9
4
3


  




8
5

8

7

1

6

6



8  
8  
8  


1
7
4

8  
8  
1
2
6

5
8



6



8

9
8  

8  
5
8  
8  
7






A
B
C
D
E
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H
I
1


3


9



2

2



4



3
5

4
2
3

8

9
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8
5

8

7

1

6

6








1
7
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7
8

1
2
6

5
8



6



8

9



5


7





For the 3rd time, the puzzle is locked. The 3rd key lies in column I with the confinement of 7 in cells I1 and I2. The candidate locations for 7 have been highlighted on the right.

Assured that the top-right block will have a 7 in I1 or I2, we can eliminate 7 from the other cells in the block: from cells H1, H2 and H3. This leaves F3 as the only cell for 7 in row 3.

11   I12 : 7 C
12   H1 / 7 B
13   H2 / 7 B
14   H3 / 7 B
15   F3 = 7 R

This is the last lock and the rest of the puzzle can be solved with the following fill steps:

16   E8 = 7 BCR
17   B3 = 6 R (Jammed step)
18   H3 = 1 NR (Jammed step)
19   G8 = 1 BC
20   I8 = 4 R (Jammed step)
21   E9 = 4 BR
22   F9 = 8 BR
23   E6 = 8 BCR
24   G5 = 4 R (Jammed step)
25   H1 = 4 BCR
26   I5 = 3 R
27   G2 = 3 C
28   D7 = 9 B
29   H7 = 3 NR
30   B9 = 3 R
31   D6 = 3 C
32   D4 = 4 BCN
33   F8 = 3 BCNR
34   B6 = 4 BCR
35   H9 = 9 B (Jammed step)
36   I9 = 2 BN (Jammed step)
37   G1 = 2 BR
38   E1 = 5 R (Jammed step)
39   H2 = 5 BNR
40   C5 = 5 R
41   I1 = 6 R
42   B8 = 5 BCR
43   E2 = 6 BNR
44   I2 = 7 BCN
45   A1 = 7 BR (Jammed step)
46   A2 = 8 BC
47   C2 = 9 BR
48   D1 = 8 BCR
49   A8 = 9 BR
50   B1 = 1 BNR
51   D2 = 1 BCNR
52   B4 = 9 BCN
53   C4 = 1 BR
54   C8 = 2 BNR
55   A9 = 1 BCR
56   C6 = 7 BC
57   E5 = 9 BCR
58   G6 = 9 BCR
59   A6 = 6 BC
60   C9 = 6 BCNR
61   E4 = 2 BCN
62   G4 = 5 BCN
63   H4 = 7 BCR
64   A5 = 2 BCNR
65   F4 = 6 BCNR
66   F6 = 5 BCNR
67   H6 = 2 BCNR



A
B
C
D
E
F
G
H
I
1
7  

3

7  
9

 7
7
2
7  
2
 7

7  
4

 7
7  
3
5

4
2
3
7  
8
7
9
4
3

7  




7  
8
5

8

7

1

6

6
7  

 7




7  
1
7
4
7
8

1
2
6

5
8



6
7  
7  

8

9



5


7




* Note that 7 is also confined in the mid-right block to cells H4 and H6. This also eliminates 7 from H1, H2 and H3 because they are in the same column as the confinement cells.
A
B
C
D
E
F
G
H
I
1
7  

3

7  
9


7
2
7  
2
 7

7  
4


7  
3
5

4
2
3
7
8

9
4
3

7  




7  
8
5

8

7

1

6

6
7  

 7




7  
1
7
4
7
8

1
2
6

5
8



6
7  

8

9



5


7





































A
B
C
D
E
F
G
H
I
1
7
1
3
8
5
9
2
4
6
2
8
2
9
1
6
4
3
5
7
3
5
6
4
2
3
7
8
1
9
4
3
9
1
4
2
6
5
7
8
5
2
8
5
7
9
1
4
6
3
6
6
4
7
3
8
5
9
2
1
7
4
7
8
9
1
2
6
3
5
8
9
5
2
6
7
3
1
8
4
9
1
3
6
5
4
8
7
9
2


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