Locked twice

Friday's Sudoku puzzle from Toronto Star gets locked twice. Here is the original puzzle on 10 October 2014 by Pappocom:

After only 7 steps it gets locked like this:

The key to this first lock lies in the first row. The last 2 cells (columns H and I) have only 3 and 8 as candidates. Thus, 3 and 8 can be eliminated from the rest of row 1, particularly in cell A1. This leaves A1 with a lone candidate, 1. Also, only one location remains to place 8 in column A, on A6.

HI1: 38 N
A1<>8 R
A1=1 N
A6=8 C

With two more steps, the puzzle is locked again.
D5=8 BC
B6=5 N

The key to the second lock lies in the 4th row. The last 3 cells (columns G, H and I) have only 1, 2 and 8 as candidates. Thus, 1, 2 and 8 can be eliminated from the rest of the block (and the rest of the row too). In particular, 1 and 2 are eliminated from cell G6, thus leaving 7 as the only candidate.

GHI4:128 N
G6<>12 B
G6=7 N
D6=2 R
F1=2 BC
H2=7 B
H7=9 C
E9=9 BC
... to the end.

Locked Puzzle 5 (from Toronto Star)

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 420080001 000509000 001060005 070000800 000106000 009000030 600020300 000704000 200090057 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

A B C D E F G H I 1 4 2 8 1 2 5 9 3 1 6 5 4 7 8 5 1 6 6 9 3 7 6 2 3 8 7 4 9 2 9 5 7 After step 6: I2=3 BC A B C D E F G H I 1 4 2 5 8 1 2 5 1 9 3 3 1 6 5 4 7 9 8 5 1 6 6 9 3 7 6 7 2 3 8 7 4 9 2 6 9 5 7 Wall ABC1 = 425 A B C D E F G H I 1 4 2 5 8 1 2 5 1 9 3 3 1 6 5 4 7 9 8 5 1 6 6 9 3 7 6 7 2 3 8 7 4 9 2 6 9 5 7 Wall DEF2 = 519 A B C D E F G H I 1 4 2 5 8 1 2 5 1 9 3 3 1 6 5 4 7 9 8 5 1 6 6 9 3 7 6 7 2 3 8 7 4 9 2 6 9 5 7 Jammed after 14 18=8 C A B C D E F G H I 1 4 2 5 3 8 7 1 2 5 1 9 3 3 1 4 6 2 5 4 7 9 8 5 1 6 6 9 2 8 3 7 6 7 8 2 3 8 7 4 8 9 2 6 9 5 7 Locked after 20 B7=5 BR A B C D E F G H I 1 4 2 5 3 8 7 1 2 5 1 9 3 3 1 4 6 2 5 4 7 9 5 8 5 1 6 6 9 2 8 3 7 6 5 7 8 2 1 3 8 3 7 5 4 8 9 2 6 9 3 5 7 Locked after 20 B7=5 BR A B C D E F G H I 1 4 2 5 3 8 7  69 69 1 2 5 1 9 x x 3 3 1 4 6 2 x x 5 4 7 9 5 8 5 1 6 6 9 2 8 3 7 6 5 7 8 2 1 3 8 3 7 5 4 8 9 2 6 9 3 5 7 Unlocked and jammed A B C D E F G H I 1 4 2 5 3 8 7 1 2 7 5 1 9 3 3 1 4 6 2 7 5 4 7 9 5 8 5 1 6 7 6 9 2 7 8 3 7 6 5 7 8 2 1 3 8 3 7 5 4 8 9 2 6 9 3 5 7 Completed A B C D E F G H I 1 4 2 5 3 8 7 9 6 1 2 7 6 8 5 1 9 2 4 3 3 9 3 1 4 6 2 7 8 5 4 3 7 6 9 4 5 8 1 2 5 8 4 2 1 3 6 5 7 9 6 5 1 9 2 7 8 4 3 6 7 6 5 7 8 2 1 3 9 4 8 1 9 3 7 5 4 6 2 8 9 2 8 4 6 9 3 1 5 7