u/Ok-Basket5408

Which white stones, and how many of them, must be removed so that black can capture all remaining white stones?

Bonus: Can the answer be extrapolated to any n x n board?

Good day!

I'd like to ask for help from this great community to analyze a new game that has me obsessed. It's called "SIX" or "SIX-O," and it's played on a hexagonal or triangular grid. The goal is to create a line, triangle, or ring of six connected stones. I think it's a much more complex game than it first appears.

At first, it might seem like another Connect 4, but as the game progresses, it transforms into a battle for territory, like Go/Baduk. I'm sharing an image of a very technical game that ended in a draw: there isn't a single six-stone triangle, line, or ring.

The original version is played without a board and only with 21 pieces of each color, which I think is a significant limitation for exploring it in depth. The version I'm exploring is played on a hexagonal grid, preferably larger than 8x8x8, and also adds another winning possibility: any ring of 6 or more stones. This eliminates most ties and allows for the emergence of interesting patterns similar to the ladders in Go/Baduk. I hope you'll give it a try.

I've been exploring other hexagonal games like Hex, HeXO (Connect-6), TriGo, Bloom, and Havannah, and in my opinion, this version of SIX-O is much more elegant. I believe that if it reaches the right community, it has the potential to become a classic, as it doesn't require a double turn or the use of other colors.

That's why I wanted to ask for your support in developing a web implementation of this game. Of course, all credit would go to whoever creates it. I feel a little sad to think that I found a super interesting and deep game that no one else knows about, so I'd like to share it with the community.

As I said, the rules are very simple: players take turns, placing stones on any square of the board (not necessarily adjacent like in the original version). The stones placed remain on the board, and the first player to achieve a line of six, a triangle, or any ring of any size wins.

The only additional rule is to balance the start: 1) White plays first and places a stone near the center; 2) Black places an adjacent stone; and 3) White must play their second stone fulfilling the following conditions: a) it cannot be adjacent to their first stone, and b) it must be adjacent to the stone placed by the opponent.

In practice, this allows Black's next move to be connecting two stones that separate White's stones (like a black bee with white wings), which balances the game: White has one more stone on the board, but Black has the initiative during the first phase of the game because their stones are connected.

And that's all. I hope you'll give the game a try, and that someone can take this project and develop it to the next level. And I apologize for my English; it's not my native language.

Thank you so much for all your support!