I was surprised to find out that you should write:

I waited for a torturous three days.

Instead of:

I waited for torturous three days.

Why is this? "Days" is plural ...

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    This is a good question. Just a side note, I think you probably mean a torturous three days, unless the three days were particularly twisty. – 1006a May 1 '17 at 15:12
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    @1006a There is also the meaning "excessively lengthy and complex"; I've certainly had days like that. – JAB May 1 '17 at 16:25
  • @JAB I've definitely had days like that, too! That's why I said probably, though I'd still prefer to use tortuous for the red tape or document analysis or medical appointments or what-have-you that make the day feel long, rather than the day itself. – 1006a May 1 '17 at 17:09
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    Think of this construction as referring to a specific period, amount, or other "unit" of something, and then the quantity describes that single aggregation. "A tortuous three days" means a single period that was three days long. It is similar to how "A 12 inch ruler" is a single ruler that is 12 inches long, only the item isn't explicitly named, only implied. – fixer1234 May 1 '17 at 17:27
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In phrases that follow this pattern:

a {modifier} {number} {plural noun relating to time}

{plural noun} is understood to be a duration.

She spent a nervous thirty minutes waiting to be interviewed for the job.

We spent a pleasant two weeks at the lake.

He worked a grueling three years in the desert.

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    Not just "{plural noun relating to time}". E.g. "I walked a good three kilometers". – MSalters May 1 '17 at 12:53
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    Yes, distances also follow the pattern. Any unit of measure. My captors injected me with a painful three ccs of snake venom. or After a day in the hot sun, I drank a needed three cups of water. – Tᴚoɯɐuo May 1 '17 at 13:06
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    The word order matters. {number (other than 1)} {modifier} {plural noun} is plural. For example, "I waited for three tortuous days" is grammatically correct. – Jasper May 1 '17 at 18:05
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    Not just units of measure. Google Book Search finds, for example, "Moreover, this solitary genre produced a mere eight works, all of remarkably similar content"; "This theater probably seated a good 200 people and it was packed"; "Moreover, many Christians — [...] — include in the Old Testament an additional six or seven books as well as certain supplements to the books of Esther and Daniel [...]"; etc. – ruakh May 2 '17 at 0:51
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    In short: Because an amount is singular, even if the amount is not 1. – ShadSterling May 2 '17 at 20:48

In general, dates & times, lengths and weights1, amount of currency and Maths expressions are not considered plural even if they use plural forms of words. Like these

Three days isn't a long time.
Three days aren't a long time.

Ten miles is too long to walk.
Five kilograms isn't heavy for him to lift.
Ten miles are too long to walk.
Five kilograms aren't heavy for him to lift.

Twenty pounds is too little to buy this.
Twenty pounds are too few to buy this.

Two plus three is five.
Two plus three are five.

So, in your case, "tortuous three days" is considered as "a duration of time", so even if the word "day" is in its plural form, we do not consider the phrase as a plural form.
If you really want to treat it as plural, you can say

I waited for three tortuous days.
I waited for tortuously three days.

In the upper way "days" will be treated as a regular noun, losing its meaning of "duration of time" because an adjective is inserted in between the number and "days".

Besides, as minnmass mentioned in comments, this rule breaks down if the measure is a part of a whole. For example:

Three days isn't a long time, unless two are rainy.

The first part of the sentence follows the rule, but the latter part doesn't, as "two" is part of the whole ("three days").

References: This and this on English.SE. A Google search query is also preferred.

1. Actually all physical measurements are never considered plural. For example, "10 Amperes is a large current" and "100 degrees Celsius is the boiling point of water" and "101325 Pascals is the standard atmosphere pressure".

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    10A is a large current; most major shops don't accept it as currency :) – hobbs May 1 '17 at 15:07
  • There is another form of putting addition of numbers into words that treats the numbers as plural: "Two and two are four." But that seems very old-fashioned to me. – David K May 1 '17 at 18:55
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    This rule breaks down if the measure is a part of a whole: "Three days isn't a long time, unless two are rainy". – minnmass May 1 '17 at 19:04
  • @DavidK If you use "and" for conjunction, then it sounds better to me being plural. But if you use "plus, minus, multiplied by and so on", singular form is better. – iBug May 1 '17 at 23:35

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