Anonymous user
Talk:Flipping bits game: Difference between revisions
→References?
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::: Added! P.S. have you seen the game before? --[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 16:04, 11 July 2013 (UTC)
:::: Don't think so. I feel I've seen something like it (enough to wonder about parity checking as a method of verification) but not the same. –[[User:Dkf|Donal Fellows]] ([[User talk:Dkf|talk]]) 14:17, 16 July 2013 (UTC)
:: You're right -- there are actually more start-end pairs that cannot be completed than start-end pairs that can. I'll give a proof that even-sized grids cannot change parity via the legal moves, and from there, I'll show what else that means.
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:::Thanks AnonymousJohn for the effort you have put into that answer. More proof that generation of the start position from legal random flips from the target position was necessary. --[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 14:14, 29 November 2013 (UTC)
::::Glad to help. I wish I could definitively prove a relationship between the starting and ending position that guarantees a solution. Alas, I don't think my proof skills are quite that good. I suspect that if the starting and ending positions share the same parity for each even-sized subgrid, there is a solution, but I'm not sure I could prove that. [[User:AnonymousJohn|AnonymousJohn]] ([[User talk:AnonymousJohn|talk]]) 01:50, 4 December 2013 (UTC)
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