Saturday’s Sudoku puzzle from Toronto Star (July 30, 2011) is jammed many times and also locked. The key to unlocking it is by using the full house elimination technique. 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
We start off with 6 easy steps: 1 C1 = 5 BR 2 C7 = 7 BR 3 D4 = 9 BC 4 D9 = 6 BC 5 E2 = 1 BR 6 I2 = 3 BC A technique in the search for the hard to find steps is to use walls. A wall is 3 filled up cells in a block that are all in the same row or column. In this stage, there are 4 walls: ABC1 = 425 DEF2 = 519 E123 = 816, and I123 = 135 I use walls to scan the other rows or columns in the block and do elimination by confinement. Using the wall ABC1=425, we can look for the numbers that are in rows 2 and 3, which are not in the top-left block. The numbers 3, 6 and 9 (highlighted) will be confined: 3 is confined to AB3 and DF1 9 is confined to AB3 and GH1 6 is confined to BC2 and GH1 The series of confinements leads to full houses: AB3 : 39 GH1 : 69 The full houses can be used for further elimination, but for now, we’ll look at the pertinent wall that reveals the jammed step: DEF2 = 519 The numbers 2 and 4 are confined because of the wall: 2 is confined to DF3 and GH2 4 is confined to D3 and GH2 We find the step D3 = 4 B. 7 D3 = 4 B After every step, we can follow through with the same row, column, block or number of the last step. Column D and the top-center block can be completed. 8 D1 = 3 CN 9 D6 = 2 C 10 D7 = 8 CN 11 F3 = 2 BC 12 F1 = 7 BCN 13 F6 = 8 BC The next step is found by using the wall I123 = 135. 14 I8 = 8 C (Jammed) At this point, the puzzle is jammed. The step is not easy to find because it requires counting off the candidate numbers for each cell. After going through the most-filled columns: E, F and I, and not finding a step, column C reveals the step C8 = 3 N and the completion of column F and the bottom-center block. 15 C8 = 3 N 16 F9 = 3 BR 17 F7 = 1 BC 18 F4 = 5 CN 19 E8 = 5 BCN One more follow-up step and the puzzle is locked. 20 B7 = 5 BR (Locked) The key to unlocking the puzzle lies in the full house that was identified earlier in GH1 and the elimination of the numbers from the rest of the block. This leaves G3 with 7 as the only candidate. 21 GH1 : 69 R 22 G2 / 6 B 23 H2 / 6 B 24 H3 / 9 B 25 G3 / 9 B 26 G3 = 7 N All the other 7s can be found easily. Thereafter, the puzzle is jammed again. 27 A2 = 7 BCR 28 H5 = 7 BC 29 E6 = 7 BCR (Jammed) The full houses in GH1 and GH2 leave only 8 as the candidate in H3. The puzzle gets jammed again, but by following through with the same number (8) we can find the next step: A5=8 C. 30 H3 = 8 N (Jammed) 31 A5 = 8 C The rest of the puzzle gets solved easily from here. 32 A6 = 5 BC 33 G5 = 5 BCR 34 I5 = 9 BR 35 C5 = 2 R 36 H7 = 9 R 37 I4 = 2 C 38 G1 = 9 BCR 39 H1 = 6 BNR 40 G8 = 6 BR 41 H8 = 2 BR 42 I6 = 6 BC 43 C4 = 6 BR 44 G2 = 2 BCR 45 I7 = 4 CNR 46 B2 = 6 BCR 47 H2 = 4 BNR 48 C2 = 8 BNR 49 G6 = 4 BC 50 B9 = 8 BCR 51 G9 = 1 BCN 52 H4 = 1 BCN 53 B5 = 4 BC 54 B6 = 1 BNR 55 C9 = 4 BCNR 56 A8 = 1 BCR 57 E4 = 4 BCR 58 A4 = 3 BNR 59 B8 = 9 BNR 60 E5 = 3 BCNR 61 A3 = 9 BCNR 62 B3 = 3 BCNR |
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
