players play the following game consisting of turns. Alice's clones and Bob's clones go in some order. After all turns have passed, there are pieces. What is the maximum number of triangles that Alice's clones can guarantee forming given that Bob's clones are working against Alice's clones?
Clarification: One possible ordering might be , which would repeat, and so for the first turns in this example, Alice's clones and Bob's clones would follow the sequence .
Instead of asking for the maximum number of triangles Alice can make, I think it might also be interesting if we ask for the minimum. What do you guys think?