Is it correct to say 'a four doored car'?

Solution 1:

If I describe a motor car as a 'four door car' I am making 'door' an adjective.

No. Although it has an adjectival function.

You are using "door" as an attributive noun that, itself, is modified by "four".

four-door = noun phrase acting attributively.

The hyphen is not necessary, but if you use it, use it consistently:

In four-door vehicles, the B-posts are located between the front and rear doors of a vehicle. Vehicle Rescue and Extrication: Principles and Practice By David Sweet

It would be true of both two and four door coachbuilt cars as well; i.e., the C pillar could be a half-pillar type stopping at the belt- or waistline (q.v.), (Illustrated Dictionary of Automobile Body Styles, 2d ed. By Lennart W. Haajanen)

Is it correct to say 'a four doored car'?

Yes, "four-doored" is an adjective but it is rare and rather formal and I have not heard it other than as a predicative adjective - "The car is four-doored." You would usually say "The car is a four-door."

Solution 2:

For whatever it’s worth, the OED has four-door for the adjective. They provide this citation:

• 1957 P. Frank Seven Days to Never i. 13
  A four-door sedan.

So probably that’s what you should say unless you mean something else than is meant by the way their citation uses it. See below for such contrasting examples using other pairs than yours.

What you write is of course up to you. These normally are hyphenated in writing when used attributively, but not always: there are still a lot of five pound notes in circulation.

Usually you have only one of either "a № NOUN something" versus "a № NOUNed something" in common use, but which it is depends on other factors.

For one thing, measure phrases used attributively seldom inflect their nouns for number the way they often do when used predicatively. So you have things like:

• a twenty-one-gun salute
• a five-acre farm
• a five-day week
• the four-colour problem
• a four-letter word
• running a four-minute mile
• a four-stroke engine
• the million-dollar question

Compare those with “more adjectival” NOUNed versions:

• a three-legged stool
• a five-fingered jack
• a game of four-handed cribbage
• some five-leaved grass
• a two-sepalled blossom
• that hundred-headed thistle

Nobody today says ❌ a five-dayed week because normally such measure phrases used attributively start out with an uninflected noun, so you only have a four-day week. But we used to say ❌ a four-inched whatever, even though we now say only a four-inch whatever.

Sometimes both versions exist. If so, they might mean the same thing the way they do in one-finger salute and one-fingered salute.

But they might also mean different things as they do in a three-foot dog versus a three-footed dog, or a five-point essay versus a five-pointed star.

It really just depends — there are incalculably many more such example pairs out there, both contrasting ones and non-contrasting ones.

Solution 3:

Both four-door car and four-doored car are correctly constructed according to English grammar rules. Which one is more idiomatic based on actual usage is a separate issue.

The use of a phrase four-doored car does not necessarily imply the existence of a verb to door. English -ed has multiple functions. It can form the simple past tense of a verb, as in They proved it. It can form the past participle of a verb, as in I have watched it before. Some adjectives, such as excited, are derived from a verbal past participle ending in -ed. But a third function of -ed is forming adjectives directly from nouns (or nominal phrases) with the meaning "possessing [noun]".

Some examples: small-minded, two-faced, cross-eyed, brown-haired.

These are all idiomatic and usual, even though it is not usual to say *"They are minded small", *"They are faced two", "They are eyed cross", *"They are haired brown". Also, there is no implication that the state is a result of some change, as there often would be with a participial adjective (describing someone as brown-haired does not imply that their hair became brown after previously being a different color).

The Oxford English Dictionary has a separate entry for this use of -ed, which says the precise details of the etymology are unclear. Some quotations:

• In modern English, and even in Middle English, the form affords no means of distinguishing between the genuine examples of this suffix and those participial adjectives in -ed [...] which are ultimately [from] nouns through unrecorded verbs

• The suffix is now added without restriction to any noun from which it is desired to form an adjective with the sense ‘possessing, provided with, characterized by’ (something); e.g. in toothed, booted, wooded, moneyed, cultured, diseased, jaundiced, etc., and in parasynthetic derivatives, as dark-eyed, seven-hilled, leather-aproned, etc.

• Groundless objections have been made to the use of such words by writers unfamiliar with the history of the language

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