Just some general musings…I was marveling at the variety of problems and patterns that have been proposed and achieved, both in the original book, as well as in the discussions here. We know that with large enough board and sufficient supply of pieces the TT can do anything a computer can, and so any finite sequence can be generated. But what about the TT as it comes out of the box?
There are 2^n possible sequences of length n. What is the largest value of n so that all 2^n sequences can be generated with the original TT set? Or, said differently, what is the shortest sequence that cannot be generated?
It seems that sequences with regularity of some sort will be easiest to generate with a smaller number of pieces, and sequences with no apparent regularity or repeating pattern will require more pieces. Perhaps that would be a place to start to find short sequences that cannot be generated.