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
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 |
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| 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 |
* 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.
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