I was a bit bored today so I decided to try to set up a position where you can go from 0 completed tasks to 20 by placing a single tile. The most I could accomplish was 17:
https://imgur.com/xLs99wA
When you place the yellow 4-tile into the hole in the middle, 17 tasks are completed.
I managed to find several other positions where 17 is doable, mostly by just switching colours. I also found a position where you can complete 18 tasks but that requires a 19th task to be completed a move earlier.
I wonder if anyone can find a 0 -> 20 position or prove such a position is impossible.
https://imgur.com/xLs99wA
When you place the yellow 4-tile into the hole in the middle, 17 tasks are completed.
I managed to find several other positions where 17 is doable, mostly by just switching colours. I also found a position where you can complete 18 tasks but that requires a 19th task to be completed a move earlier.
I wonder if anyone can find a 0 -> 20 position or prove such a position is impossible.