_m_k wrote:Leon1789:
Will you please explain the following? It sounds interesting and I like to learn in detail.
10 contradiction nets using singles and locked sets in 0-level recursion
f7#1, b7#8, c6#1, c5#8, f3#1, c9#3, a4#3, h7#4, k7#5, a8#3, finished
C#z means C=z is a disproved move by a contradiction net using singles, triples, quads... so -zC is proved.
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123456789
+----------
A |1.......2
B |.3..4..5.
C |..6...7..
D |...1.3...
E |.8..7..4.
F |...4.6...
G |..2...6..
H |.5..3..8.
K |9.......1
Starting point : try f7=1 and find a quick contradiction (using singles, triples, quads). So f7#1 definitively.
Now, try b7=8 and find a contradiction. So b7#8 definitively.
And so on... c6#1, c5#8, f3#1, c9#3, a4#3, h7#4, k7#5, a8#3, and finish (using singles, triples, quads).
At the end, a unique solution is find and proved , and there are no recusion, but only 10 iterative steps :
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if f7=1
then contradiction
therefore f7#1
if b7=8
then contradiction
therefore b7#8
if c6=1
then contradiction
therefore c6#1
...
if a8=3
then contradiction
therefore a8#3
finally a singles,triples,quads application leads to a solution
The "2 backdoor guess" does not prove the uniqueness of the solution : for me, it's a big difference between a simple guessing (no proof) and a dynamic forcing chain (valid proof).
I will post solutions for the five puzzles, but they are a little bit hard. Here, 1-level recursion is obligatory.