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What can we deduce from the M matrix?
1 2 3 4 5 6 7 8 9
.---------.---------.---------..---------.---------.---------..---------.---------.---------.
a |12 6 9|12 6 | 2 6 9||1 5 | | || 2 56 9| | | a
b |12 4 6 8 |12 4 6 8 | 2 6 ||1 5 | | || | 56 8 | 2 6 8 | b
c | | | || | | || | 89| 89| c
|---------+---------+---------++---------+---------+---------++---------+---------+---------|
d | |1 3 6 | ||1 89|1 3 8 |1 6 9|| | | 6 9| d
e |123 6 |123 6 | ||1 5 7 9|1 3 |12 567 9|| | 3 567 9| 67 9| e
f | 23 6 | | || 45 7 | 34 | 2 567 || 56 | 3 567 | | f
|---------+---------+---------++---------+---------+---------++---------+---------+---------|
g | 4 6 89| 4 6 8 | || | 4 8 | 7 9|| | 6789| | g
h | 234 6 89| 234 6 8 | ||1 4 89| |1 9|| 2 6 9|1 6 89| 2 4 6 89| h
i | 2 4 89| | 2 9|| | |1 7 9|| 2 9|1 789| 2 4 789| i
'---------'---------'---------''---------'---------'---------''---------'---------'---------'
1 2 3 4 5 6 7 8 9
Cells a4 and b4 both contain 1 and 5.
And they contain ONLY 1 and 5.
Clearly, a4 = 1 if and only if b4 = 5.
And a4 = 5 if and only if b4 = 1.
We say a4 and b4 "monopolize" the values 1 and 5.
No other cell in column 4 can contain the values 1 and 5.
These are called "twins".
New problem statement:
sudoku Pok Jour 060507 Five Dark Stars
000078040 000090700 503004100 700000420 004000800 098000001 001200305 007050000 05036000030
run
* a4, b4 monopolize 15 =>
not d4 e4 f4 h4 1 5
run
end
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