I also read the rules incorrectly because of the following example:
04824: 0 Torf
04824: 0 fort
04824: 0 Tor 4
The last solution is what lead me astray. If it had read:
As you work left to right, if at any point a word can be inserted - using a digit is illegal and at no point can two digits be adjacent
I would have understood much better. In any event, my solution is buggy and produces incorrect results. Since it seems like you were after approaches, I believe mine is interesting because of the unrestricted integer partitions. I have no interest at this point in making it a correct solution.
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