Monday, 30 May 2011

Locked Puzzle 2

Sunday’s Sudoku puzzle from Toronto Star (May 29, 2011) is a good example of a locked puzzle. Its key is elimination by confinement. 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,  May 29, 2011
Page IN2
Level: Hard

010200003
600008000
005061700
060005800
050000010
007800060
003680200
000900004
200004070

A
B
C
D
E
F
G
H
I
1

1

2




3
2
6



8


3


5

6
1
7

4

6



5
8


5

5




1

6


7
8



6

7


3
6
8

2

8



9



4
9
2




4

7




 1             F5 = 6 BCR
 2             F7 = 7 N
 3             G1 = 6 BR
 4             I9 = 6 C
 5             C8 = 6 BCR
 6             F1 = 9 N
 7             H8 = 8 B
 8             I3 = 8 C
 9             B8 = 7 N
 10          B9 = 8 C
 11          H4 = 3 C (Jammed)

The puzzle is jammed at this point and only a fill step is possible.

A
B
C
D
E
F
G
H
I
1

1

2

9
6

3
2
6



8


3


5

6
1
7
8
4

6



5
8
3

5

5


6
1

6


7
8



6

7


3
6
8
7
2

8

7
6
9


8
4
9
2
8



4

7
6



12           A1 = 7 BC
 13          A5 = 8 C
 14          C1 = 8 BR (Locked)

There are no more fill steps: the puzzle is locked. Elimination steps are necessary to unlock the puzzle.


A
B
C
D
E
F
G
H
I
1
7
1
8
2

9
6

3
2
6



8


3


5

6
1
7
8
4

6



5
8
3

5
8
5


6
1

6


7
8



6

7


3
6
8
7
2

8

7
6
9


8
4
9
2
8



4

7
6



In the left-middle block, 3 is confined to A6 and B6. Therefore, 3 can be eliminated from the rest of row 6, particularly in E6 and F6. This opens 2 fill steps: with 2 as the only possible digit in F6, and F8 as the only location for 3 in column F.

15           AB6 : 3 B
16           E6 / 3  R
17           F6 / 3  R (The Key)
18           F6 = 2 N
 19          F8 = 3 C
 20          E8 = 2 BCR (Jammed)

The puzzle is jammed again and only a fill step is possible.


A
B
C
D
E
F
G
H
I
1
7
1
8
2

9
6

3
2
6



8


3


5

6
1
7
8
4

6



5
8
3

5
8
5


6
1

6


7
8



6

7


3
6
8
7
2

8

7
6
9


8
4
9
2
8



4

7
6

21           G9 = 3 BCR (Jammed)

The puzzle is jammed for the third and last time. The good thing about two jams-in-a-row is that the second one is easier to find, because it is related to the previous step by being in the same row, column or block, or involving the same digit. In this case the second jam shares the same row as the previous one.


22           C9 = 9 R


A
B
C
D
E
F
G
H
I
1
7
1
8
2

9
6

3
2
6



8


3


5

6
1
7
8
4

6



5
8
3

5
8
5


6
1

6


7
8

2

6

7


3
6
8
7
2

8

7
6
9
2
3
8
4
9
2
8



4

7
6



23     C4 = 1 C
24     B7 = 4 N
25     C5 = 2 B
26     D9 = 1 C
27     E6 = 1 BR
28     I4 = 2 R
29     C2 = 4 CN
30     D2 = 5 C
31     E9 = 5 BNR
32     I5 = 7 BC
33     D4 = 7 C
34     E1 = 4 N
35     E2 = 7 BR
36     H1 = 5 BR
37     A4 = 4 R
38     B2 = 3 R
39     D3 = 3 BN
40     D5 = 4 BC

 41    E4 = 9 N
 42    E5 = 3 C
 43    H3 = 4 BCR
 44    H7 = 9 N
 45    A3 = 9 N
 46    A6 = 3 BCR
 47    B3 = 2 BCR
 48    B6 = 9 N
 49    G5 = 9 NR
 50    G6 = 4 BCR
 51    H2 = 2 BCNR
 52    G2 = 1 N
 53    G8 = 5 C
 54    I2 = 9 BCR
 55    I6 = 5 BNR
 56    A7 = 5 BCR
 57    A8 = 1 NR
 58    I7 = 1 BCN




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






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