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Talk:Knight's tour: Difference between revisions
→The 7x7 problem: updated results + comment on pattern of failure on 7x7
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:: This shows a summary of results for 5 tries at each starting position:
<pre>Results of tests for N=7 :
Starting Square | a1 a2 a3 a4 b2 b3 b4 c3 c4 d4 *All*
*
RothTieBreaker | 70.00% 0.00% 70.00% 0.00% 90.00% 0.00% 80.00% 90.00% 0.00% 100.00% 50.00%</pre>
:: The notable thing about the pattern of failure in 7x7 is that tours started every other square fail and this shifts by one every rank. The symmetries of the squares above hold for all tie breakers and the overall pattern of failure is a cross-hatching.
:: Looking at two cases where the start was a1 and a3, the a1 failed and a3 start did not (Random Tie Breaker). Both case went through a1 but the one starting in a3 went through a1 on move 37. Looking at the ties, there was no obvious choice that would have produced a tour. The start in a1 would have had to violate the accessibility filter to succeed. That is a1, b3, c1, a2, b4, ... fails vs. a1, b3, c1, a2, c3, ... succeeds. In the later case c3 was chosen not from the ties but from the group with the highest accessibility. I'll have to dig into this a bit more later. What I did add was a log like this showing the move, minimal accessibility, and moves in that group. This is for the failing a1:
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