Essentially, Puzzle 39 is about, starting with blue input, have the output as 3 blue and 1 red repeating. Is it possible to do the same thing with n blue and 1 red repeating? I have found solutions for n=1, 2, 4, 5, 6, 8, 9, 10 and 12 (see separate posts). However, despite numerous fruitless attempts, I have not been able to come up with a solution for n=7.

Incidentally, I did come up with a “cheat” solution by using the n=6 solution and arranging the red input to have 1 blue and 1 red repeating, and ensuring that two balls come from the “red” side of the input (simply use a bit piece set in the ‘1’ position on the red input side of the board).

So, is a solution for n=7 possible? I am happy to throw this open to the community as an extra challenge.