Puzzle 60 solution - 40 parts

[Samuel]

The solution is similar to the book solution, but with a different gear set up on the right side of the board. We alternate decrementing the registers until one reaches 0, starting with A.

If a ball goes through a register with value greater than 0, it continues to the latch at the left of the gear chain and reaches the bottom of the board, summoning a ball of the other colour.

If register B reaches 0 first, the gears are in their starting position so a ball can run down the right hand side to G.

If register A reaches 0 first, the ball goes through the central gear bit, flipping the gear orientation, then summons a red ball for register B.

If register B is 0, the rightmost gear now points left and the ball is deflected into E.
If register B is still greater than 0, the latch is now broken and the ball instead runs down the left edge to L.

https://www.lodev.org/jstumble/?board=00llllr0r0eerrlleerxrfagagaeelaxrelrllllexllieilie0

[paul]

You did it! Way to go!! I spent a long time trying to figure out how to make this work. I wasn’t even sure it was possible to fit on the board. Did you think it was the hardest puzzle or was it just me?

[Samuel]

It is definitely the hardest. If register A hits 0 first, you have to trigger two separate changes, directing the B=0 line from G to E and the A>1 line to L, neither of which are obvious at the start of the problem. It is quite tricky to do and there isn’t much space to do it in.

The registers block the top of the board and the bottom rows are needed to line up with the outputs. I don’t think it is possible to use any of the empty triangle on the left - you need a latch on the A>0 line, as it will be used multiple times in one direction then at most once in a different direction, but if that latch were any further to the left, E would be blocking it from getting to the bit at the bottom. There is only just enough room left.