This is a variation of List of US-states without common letters . This is supposed to be more difficult and challenging than the original problem.
Create a list of US-States, one name per line, such that no two consecutive States in the list do contain any common letter (and such that each State occurs at most once).
This is an example:
You have 2 tasks:
- Determine the maximum number $N$ of States in such a list.
- Determine the maximum number $L$ of letters in such a list (that is, the sum of the lengths of all the States' names in the list).
The second task is probably more difficult than the first one. I will accept only answers with a complete solution. If nobody comes up with a solution within 72 hours, I will add a hint.