The task:
You are standing in front of a gigantic forest of syntax trees. One tree looks more fascinating than the other. In front of the forest is a sign:
"Every tree in this forest arises from a derivation with exactly two steps and has exactly 2021 leaves."
If you can figure out how many different trees are in the forest, you can pass. It is known that all possible trees are also present in the forest. Furthermore, two trees are considered to be the same if their structure is the same.
How many decimal places does the number you are looking for have?
I think i am near the answer but doing something wrong.
I have 2021 trees that look like this:
S->AB
A->a, B->b^2020 or A->a^2, B->b^2019 or ... A->a^2020, B->b
There must be more possibilities for e.g S->A->a^2021 (which would be only one more tree) or S->ABC->a,b,c^2019 (but in how many trees would that result?) and so on
