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    $\begingroup$ now we're cookin! +1 sweet. if someone beats 111, I will be surprised. My best was also 111, although quite a bit different than this exact solution. $\endgroup$
    – JLee
    Commented Jul 15, 2022 at 14:00
  • $\begingroup$ @JLee Yeah on second thought 110 is unlikely, though I wouldn't say out the question. I'm going to try and either find some other 111s, or try prove 110 possible/impossible :) $\endgroup$
    – Beastly Gerbil
    Commented Jul 15, 2022 at 14:02
  • $\begingroup$ If anyone finds 110, I will throw them 100 pts (not like you need it! haha) $\endgroup$
    – JLee
    Commented Jul 15, 2022 at 14:05
  • $\begingroup$ @JLee added a rough proof that 111 is optimal, it's by no means thorough, but I think its intuitive enough to show 110 is not possible $\endgroup$
    – Beastly Gerbil
    Commented Jul 15, 2022 at 14:30
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    $\begingroup$ @JLee improved my 'proof' if you can call it that, much easier to read. I'm incredibly confident that 111 is optimal - the only real tricky bit is showing that the pink squares must be a +3 $\endgroup$
    – Beastly Gerbil
    Commented Jul 15, 2022 at 15:34