The Fitter,
Glenn made some basic deductions on the initial puzzle before he wrote out the list of candidates for each cell in the grid. From the initial position, my solver suggests:
The value 3 in Box [3,1] must lie in Column 3.
- The moves (7,1):=3 and (8,1):=3 have been eliminated.
The value 8 in Box [2,3] must lie in Column 7.
- The moves (4,8):=8 and (5,8):=8 have been eliminated.
Consider the chains (1,8)~4~(1,1)-4-(7,1)~4~(7,9) and (1,8)-4-(2,9)~4~(7,9).
When the cell (7,9) contains the value 4, one chain states that the cell (1,8) contains the value 4 while the other says it doesn't - a situation that is clearly illegal.
Therefore, the cell (7,9) cannot contain the value 4.
- The move (7,9):=4 has been eliminated.
The values 1, 4 and 8 occupy the cells (7,8), (9,8) and (9,9) in some order.
- The moves (7,8):=6, (9,8):=6, (9,9):=3 and (9,9):=6 have been eliminated.
Since none of the moves listed as eliminated by the solver appears in the grid written out by Glenn, it's almost certain he made the same deductions himself.
Glenn,
The software is written in Java. Source is available at
http://sf.net/projects/sudoku (GPL) and an applet is hosted at
http://act365.com/sudoku. I took the log from a beta version of the next release - the current release won't do such a good job. Solve time is about 0.5s.
The Daily Telegraph used the term 'Diabolical' to describe puzzles that (in the opinion of the author) could only be solved through trial-and-error. With this in mind, I reran my solver with the chain-searching routines disabled. After 0.03s (i.e. much faster than before - chain-analysis is very slow), it came back with:
The value 3 in Box [3,1] must lie in Column 3.
- The moves (7,1):=3 and (8,1):=3 have been eliminated.
The value 8 in Box [2,3] must lie in Column 7.
- The moves (4,8):=8 and (5,8):=8 have been eliminated.
The cell (5,5) is one of 2 candidates for the value 2 in Column 5.
The move (5,5):=2 would lead to a contradiction.
The value 3 is the only candidate for the cell (5,5).
The rest of the puzzle follows easily from here. The question is - how long would it have taken you to discover that the move (5,5):=2 leads to contradiction? The answer is 9 moves - quite a few if you only have the newspaper, a pencil and an eraser.
1. The value 3 is the only candidate for the cell (1,5).
2. The value 2 is the only candidate for the cell (3,6).
3. The cell (4,1) is the only candidate for the value 2 in Row 4.
4. The cell (1,2) is the only candidate for the value 2 in Row 1.
5. The value 9 is the only candidate for the cell (2,3).
6. The value 4 is the only candidate for the cell (2,2).
7. The value 5 is the only candidate for the cell (1,1).
8. The value 8 is the only candidate for the cell (3,2).
9. The value 6 is the only candidate for the cell (7,2).
It's hard to escape the conclusion that this puzzle is too difficult for a newspaper.
