An entry in Fortnightly Topic Challenge #48: Unusual tag mix
I was looking at the unusual tag mixes post, and one of the ones listed is combinatorics and english. I thought "who's going to be silly enough to blend those?". +15 points for correct answer: this guy!
Here's the question: how many different grammatically correct simple sentence diagrams can be made starting with the base sentence "bludgeons humanise", and using all four of the words "blonde", "nigh", "midst", and "abaft"?
Note that I use "sentence diagram", instead of sentence, because what we're really counting is the number of ways these six words can relate to each other as parts of speech, ignoring the complications of making an actual sentence out of them. This would generally involve the addition of connecting words and articles, but we do not wish to consider those here.
- The sentence diagram should be for a simple sentence, having one independent clause with subject "bludgeons" and verb "humanise".
- For the purpose of this puzzle, the words given can be used as the following parts of speech, independent of context:
- bludgeons: noun
- humanise: verb
- blonde: noun, adjective
- nigh: adjective, adverb, preposition
- midst: noun, preposition
- abaft: adverb, preposition
- Word ordering is irrelevant here, so "quick brown fox" and "brown quick fox" are considered the same. All that matters is the "what modifies what" relationships, much as is usually displayed in a sentence diagram. This includes ordering within the diagram.
- Adjectives modify nouns.
- Adverbs modify verbs, adjectives, or other adverbs.
- Prepositions must have a noun object, which may itself be modified by an adjective, which may itself be further modified.
- A prepositional phrase may be used as either an adjective or an adverb, and may as a whole be modified according to the rules of the part of speech it is taking on.
- The verb may be used either transitively or intransitively.
"abaft" is an adverb, which is modifying the verb "humanise". The adverb "abaft" is modified by the prepositional phrase "midst blonde", acting as an adverb. The noun "blonde", as an object of a preposition, is being modified by the adjective "nigh". To make this into a "real" sentence, it would read something like "Bludgeons become more human behind the middle of a nearby blonde."
Again "abaft" is an adverb, which is modifying the verb "humanise". The adverb "abaft" is modified by the prepositional phrase "midst blonde", acting as an adverb. But now the prepositional phrase "midst blonde", acting as an adverb, is being modified the adverb "nigh". This might be realized via "Bludgeons become more human behind the nearby middle of a blonde."
The meaning difference is subtle, but potentially important for the blonde, since the former implies the integrity of the blonde (since the blonde is nearby), but the latter only insists that the middle of the blonde be nearby.
As with any "real" combinatorics problem, there is some case bashing involved, but I hope the context keeps it interesting. I hope you enjoy!