I wanted to run the machine pretty much constantly pulling QS but evaluation of the state machine takes a long time, which pains me. I theorize maybe some heavy reworking could save 20-30 on this, so I won't be too surprised if the top solves are sub-400. I'm excited to see how I'm blown out of the water.

The first two bits are +3 each on the high and low order digits on the output. This partitions the space into 4 chunks of 9, only 8 of which need to be mapped. The remaining 3 bits have 8 cases, so we just need a mapping from those 3 bits to 8 output cases. The mappings are restricted to base-3 as required by the partitioned space, so you can imagine the 3 bits counting up in binary while at the same time you have 2 digits counting up in base-3, from 00 to 21.

Small disclaimer, the 3 bits do not count like you think since they are not in order from high-low as usual. The last 3 bits are actually in the order (2 1 4) instead of the typical (4 2 1), thus the mapping is a little mixed up. This is done for convenience of implementation for the state machine, as 2 is required to go first and that leaves only the end as a convenient location for 4.

State machine concept is pulled from past computations, although it's only really used as a state machine for the last 3 bits, the first 2 utilize the stick but are not a part of setting state. I won't go into precisely how it works here since this is already long, so hopefully hosts can explain it or someone else with a similar solve has already shown the idea.


===== 'VIDEO TAPE' =====
 0.	salt-salt-salt-salt-salt	 => 	Lead-Lead
 1.	salt-salt-salt-salt-FIRE	 => 	Tin-Tin
 2.	salt-salt-salt-FIRE-salt	 => 	Tin-Lead
 3.	salt-salt-salt-FIRE-FIRE	 => 	Iron-Tin
 4.	salt-salt-FIRE-salt-salt	 => 	Iron-Lead
 5.	salt-salt-FIRE-salt-FIRE	 => 	Lead-Iron
 6.	salt-salt-FIRE-FIRE-salt	 => 	Lead-Tin
 7.	salt-salt-FIRE-FIRE-FIRE	 => 	Tin-Iron
 8.	salt-FIRE-salt-salt-salt	 => 	Lead-Copper
 9.	salt-FIRE-salt-salt-FIRE	 => 	Tin-Silver
10.	salt-FIRE-salt-FIRE-salt	 => 	Tin-Copper
11.	salt-FIRE-salt-FIRE-FIRE	 => 	Iron-Silver
12.	salt-FIRE-FIRE-salt-salt	 => 	Iron-Copper
13.	salt-FIRE-FIRE-salt-FIRE	 => 	Lead-Gold
14.	salt-FIRE-FIRE-FIRE-salt	 => 	Lead-Silver
15.	salt-FIRE-FIRE-FIRE-FIRE	 => 	Tin-Gold
16.	FIRE-salt-salt-salt-salt	 => 	Copper-Lead
17.	FIRE-salt-salt-salt-FIRE	 => 	Silver-Tin
18.	FIRE-salt-salt-FIRE-salt	 => 	Silver-Lead
19.	FIRE-salt-salt-FIRE-FIRE	 => 	Gold-Tin
20.	FIRE-salt-FIRE-salt-salt	 => 	Gold-Lead
21.	FIRE-salt-FIRE-salt-FIRE	 => 	Copper-Iron
22.	FIRE-salt-FIRE-FIRE-salt	 => 	Copper-Tin
23.	FIRE-salt-FIRE-FIRE-FIRE	 => 	Silver-Iron
24.	FIRE-FIRE-salt-salt-salt	 => 	Copper-Copper
25.	FIRE-FIRE-salt-salt-FIRE	 => 	Silver-Silver
26.	FIRE-FIRE-salt-FIRE-salt	 => 	Silver-Copper
27.	FIRE-FIRE-salt-FIRE-FIRE	 => 	Gold-Silver
28.	FIRE-FIRE-FIRE-salt-salt	 => 	Gold-Copper
29.	FIRE-FIRE-FIRE-salt-FIRE	 => 	Copper-Gold
30.	FIRE-FIRE-FIRE-FIRE-salt	 => 	Copper-Silver
31.	FIRE-FIRE-FIRE-FIRE-FIRE	 => 	Silver-Gold