"How did it use/d to work?"; 'use' or 'used'?

In the above sentence I'm having trouble deciding between use & used.
If I go to verbalise it the d is definitely dropped, but that could just be a locale thing and written it would still contain the d.

The issue [for me] comes from the use of did to already set a past tense, so used sounds odd (whereas elsewhere it seems fine; "itusedto work by...").
Every dictionary entry I found of this verb-form of use used used for their example sentences, like above;

• He used to go every day.
• this road used to be a dirt track

But none of these were posed as questions nor was the tense specified with did or had, so I don't know if they can be used as 'it is always "used", no matter what'.

Some people recognise this in other structures where you drop the tense on the verb;

• Did you kept-? Did you keep-?
• Did you wanted-? Did you want-?
• Did you found-? Did you find-?

_{(Interestingly I feel Had you found- to be perfectly acceptable, so maybe it's more that it's a question than double past tense?)}

So, are they both acceptable? One over the other? Spoken one way, but written as the other?

Solution 1:

The uncertainty probably arises because "used to" and "use to" are homophonous, but in fact only "I used to go every day" and "This road used to be a dirt track" are correct.

The crucial point is that the aspectual verb "use" has no present tense, only infinitival and past forms, so although the form "use" appears to be a present form, it is in fact the plain (infinitive) form, which is only used in negatives and with inversion in examples like: "I didn’t use to smoke"; "Did he use to smoke"?

There is the added complication that "use" can be a lexical verb or an auxiliary one, though the books tell us that most speakers treat it as a lexical one. I suspect that’s due to the unacceptability for most people of the auxiliary use found in: %"Used you to smoke"? and %"Smoking usedn’t to be allowed".

Solution 2:

English has two idiomatic constructions, both spelled used to,
and also both pronounced /'yustu/ or /'yustə/ -- never /'yuzdtu/.

One is the transitive predicate adjective be used to, always with an auxiliary be,
which means 'be accustomed to', and which can take a gerund complement clause.

• I'm used to smoking three packs a day.

The other one, which is relevant here, is the past auxiliary construction
used to Vinf, which takes an infinitive complement.

• I used to smoke three packs a day.

This construction asserts that something was true in the past, and presupposes that it is
not true in the present. That's why the two sentences above are close to opposite in meaning.

There are no problems with either idiom in real (i.e, spoken) language;
it is only in spelling that there is a problem, and it is an insoluble one.

In both cases, used to has been reified -- joined together into a single word, like to and gather, or may and be, are joined into the single words together and maybe. This happens all the time; it's how idioms are formed. In language.

But spelling is different. Most if not all English readers have learned that

1. used is how the past tense and past participle forms of the verb use are spelled
2. In a question without an auxiliary verb, one inverts the subject and auxiliary verb
3. If one needs an auxiliary verb to invert and there is none, one inserts (and inverts) do
   (this is called Do-Support)
4. do is an auxiliary verb that takes an infinitive complement.
5. use is how the infinitive form of the verb use is spelled

But used to is the fixed spelling for the /'yustu/ pronunciation, in both idioms
(rather than /yuzd tu/, as in Shovels were used to dig this entrance tunnel).
So if it isn't spelled used to, it won't be pronounced or recognized right.

But, yet again, auxiliary do requires an infinitive complement, and used just can't be one.
The result is that while

• /hi 'dɪdṇ yustə 'du ðæt/

is perfectly grammatical and ordinary spoken English, neither one of these ways to spell it is correct,

• *He didn't used to do that.
• *He didn't use to do that.

in the sense that a fluent reader of English is likely to trip over both of them. They just don't look right. This is a problem in the spelling system only, not the language. The language has no problem at all.

The first looks bad because used looks like a misspelled infinitive,
and the second because use is pronounced /yuz/, not /yus/.

The workaround is to avoid using used to in sentences with Do-Support -- but only in writing.

Solution 3:

In the latter three, the 'Did' places you in the past tense. You say "Did you find....?," not "Did you found.....?"