Monday, 20 June 2011

Locked Puzzle 3 (from Toronto Star)


Sunday’s Sudoku puzzle from Toronto Star (June 19, 2011) is another 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, June 19, 2011
Page IN2
Level: Hard

000009016
501000003
000058090
907000020
010000030
030000907
080360000
200000304
150700000


There are 7 initial steps and 3 of which are not so easy to spot.

1      B2 = 9 BR
2      C9 = 3 BR
3      D3 = 1 BR
4      E1 = 3 B
5      F4 = 3 C
6      G1 = 5 BR
7      I3 = 2 N

The puzzle gets jammed after step 8.
8      A3 = 3 BCR (jammed)
9      B1 = 2 C


10     A1 = 7 R
11     D1 = 4 N
12     A7 = 4 N
13     B8 = 7 BC
14     C1 = 8 BNR
15     G3 = 7 R
16     C7 = 9 N
17     C8 = 6 B
18     H7 = 7 BCR
19     B3 = 6 BR
20     C3 = 4 N
21     I9 = 9 BC
22     B4 = 4 BCN
And now the puzzle is locked!

A
B
C
D
E
F
G
H
I
1




9
1
6
2
5
1




3
3



5
8
9
4
9
7



2
5
1




3
6
3



9
7
7
8
3
6



8
2




3
4
9
1
5
7





First steps
A
B
C
D
E
F
G
H
I
1



3
9
5
1
6
2
5
9
1




3
3


1
5
8
9
2
4
9
7

3
2
5
1




3
6
3



9
7
7
8
3
6



8
2




3
4
9
1
5
3
7










Locked Puzzle

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





3
3
3
6
4
1
5
8
7
9
2
4
9
4
7


3

2

5

1




3

6

3




9

7
7
4
8
9
3
6


7

8
2
7
6



3
4
9
1
5
3
7




9




The key to unlock the puzzle is by analyzing the possible locations for 1. The cells have been highlighted in the figure on the right.

Note that in the center-right block, 1 is confined on row 4 to G4 and I4. This eliminates 1 from the rest of row 4, particularly in E4.

Similarly, 1 can be eliminated from F7 because 1 is confined to G7 and I7 in the bottom-right block.

The elimination of 1 from E4 leaves 8 as the only candidate in E4. This unlocks the puzzle.
23     GI4 : 1 B
24     E4 / 1  R
25     E4 = 8  N

The remainder of the steps to complete the puzzle are:
26     D8 = 8 BC
27     I5 = 8 C
28     A5 = 6 N
29     A6 = 8 BCR
30     D5 = 9 C
31     E8 = 9 BR
32     H8 = 5 N
33     E6 = 1 C
34     F7 = 5 BR
35     F8 = 1 NR
36     G5 = 4 N
37     I4 = 5 BC
38     I7 = 1 N
39     C5 = 5 R
40     D4 = 6 N
41     D6 = 5 BC
42     E9 = 4 C
43     F6 = 4 BR
44     G2 = 8 N
45     G4 = 1 BCR
46     G7 = 2 NR
47     H2 = 4 BCR
48     H6 = 6 N
49     C6 = 2 BCNR
50     D2 = 2 CN
51     F2 = 6 BCR
52     F9 = 2 BNR
53     G9 = 6 BCNR
54     H9 = 8 BCNR
55     E2 = 7 BNR
56     E5 = 2 BCR
57     F5 = 7 CN

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





3
3
3
6
4
1
5
8
7
9
2
4
9
4
7

1
3
 1
2
1 
5

1




3

6

3


 1
 1
9

7
7
4
8
9
3
6
1 
1
7
1 
8
2
7
6

1
 1
3
4
9
1
5
3
7




9


The elimination of 1 from E4 and F7 can also be made by observing columns G and I. Along these 2 columns, 1 can only be placed along rows 4 and 7. Therefore, 1 can be eliminated from the rest of rows 4 and 7 (E4 and F7).
+
Yet another way is to observe rows 6 and 8. Along these 2 rows, 1 can only be placed along columns E and F. Therefore, 1 can be eliminated from the rest of columns E and F (E4 and F7).
A
B
C
D
E
F
G
H
I
1
7
2
8
4
3
9
5
1
6
2
5
9
1
2
7
6
8
4
3
3
3
6
4
1
5
8
7
9
2
4
9
4
7
6
8
3
1
2
5
5
6
1
5
9
2
7
4
3
8
6
8
3
2
5
1
4
9
6
7
7
4
8
9
3
6
5
2
7
1
8
2
7
6
8
9
1
3
5
4
9
1
5
3
7
4
2
6
8
9





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