With only 17 parts, no blue bits, and no crossovers, create a board that outputs in the bottom the number of blue balls specified in a 6-bit register in binary, and intercepts the next ball.
Below is link for a 5-bit register, with 14 parts (not counting the register). If I knew how to specify the size of the board exactly, I think it could be extended to a 6-bit register with 17 parts. The next standard size up in the simulator is too tall, necessitating more than 17 parts just to shuttle balls to the bottom. Is this what you had in mind?
If you create your register this way you can save some parts (register + 10) and even extend to a 7-bit counter on a regular board. Prepare to have 127 blue balls available