grammar - How to express must be in past tense in an inference

How do I express something like below in correct grammar:

If he is 21 this year, he must be 20 last year.

The problem is that I want to express that his being 20 is in the past tense. It doesn't feel right to say he must have been 20.

Searching around in ESL, I found related questions (but the answers don't apply): Past tense of "must" when meaning logical probability , whose answer suggest to use must have been; Is "must" ever grammatical as a past tense verb? , whose answer suggests to use had to. But he had to be 20 doesn't sound right either.

Answer

It really has to be

If he is 21 this year, he must have been 20 last year.

because the past tense applies logically to "he be 20 last year". Using an adverb to express the "must" part, we'd have

Necessarily, if he is 21 this year, he was 20 last year.

where the past tense of the clause "he be 20 last year" is expressed by using the past tense form of "be", which is normal in English.

When instead of "necessarily", we use "must", you might expect the second clause to be expressed

*He must was 20 last year.

But here we run into some idiosyncrasies of English grammar. You can't have a tensed verb like "was" following a modal verb; English permits only tenseless, i.e. non-finite, verb forms after a modal. And in a position where a tense inflection is not allowed, a present tense is just lost, but a past tense is converted to perfect "have". That's why we get "He must have been 20 last year". This is not logically a perfect; it's a substitute for a past tense which otherwise could not be expressed.

You can also see this conversion of a past tense to a perfect in some infinitive verb complements. "Believe" takes either a "that"-clause complement or an infinitive complement:

I believe that Mars is red.
I believe Mars to be red.

Notice that the present tense of "is" is simply not expressed in the infinitive form. But in a past tense complement,

I believe that Mars was watery at one time.
I believe Mars to have been watery at one time.

the logical past tense turns up as a perfect, because a tense is not permitted in a "to"-infinitive in English.