New 6th row single-stone template discovered

Public forum discussion.

#1 · Mason Mackaman

14 Oct 2023

#2 · Arek Kulczycki

19 Oct 2023

I think doing the "Tom's move" multiple times generalizes to connect a single stone at any row, given sufficient space. Or am I wrong? The above seems to just do "the move" twice when needed. Would be an interesting abstract exercise to find how much space is needed for any given row, but the technique is very easy.

#3 · brzytwa

19 Oct 2023

It's even unknown, if for every row a single stone is connected.

#4 · Arek Kulczycki

20 Oct 2023

Indeed it's even likely that it's not connected if we talk about an infinite board with just 1 side. I'm a hex practitioner not a theoretician and my brain was limited to include the presence of an opposite side :)

#5 · Mason Mackaman

1 Nov 2023

This template has been used to show the existence of a 7th row single stone template. It's currently being worked on, with progress updates in the hex discord. At the moment, the smallest it has been proven has a size 21 carrier, and it seems likely it won't go any smaller.

#6 · Mason Mackaman

5 Nov 2023

It has been whittled down to size 17!

#7 · richyfourtytwo

5 Nov 2023

So it'll be relevant on 19x19? Wow, great stuff!