Main answer

First, I'd like you to take a look at the example sentences from the two links you provided (1, 2):

Jack has 3 times as many sweets as John.

Sheila has 5 times as many markers as dave

Now, compare those to the sentence fragment you're trying to interpret:

$x$ is 3 times as $y$

Notice anything different? The key difference here is that, in the examples "as" occurs twice, but in your fragment there is only one "as".

In fact, your fragment (assuming, as you are, that $x$ and $y$ are nouns) is not grammatical in English. It doesn't make sense. So we must look for another interpretation.

The construction in English works as follows:

(nounA) is 3 times as (quality) as (nounB).

This is the form used in both your links. As I've mentioned, there are two instances of the word "as". In other languages we use different words for these two functions, so let's label them for clarity:

(nounA) is 3 times as¹ (quality) as² (nounB).

The first, "as¹", introduces a quality that is being compared (how tall, how heavy, how many markers, how many minutes past ten etc.), while the second, "as²", introduces what is being compared - the "baseline" for the comparison.

But, I hear you ask, there is only one "as" in the puzzle - so is it as¹ or as²?

Good question!

In English, in this sort of sentence, it is permissible to have just one "as" but only when that is an as¹.^* In this case, what we are comparing against is unstated and implicit - it must be inferred from the context, and is usually "the thing we are currently talking about". For example:

• Fred is 3 times as tall. (As me? As a normal person? As he was yesterday? Depends what we're talking about.)
• Jack has 3 times as many sweets. (As John? As me? As he did yesterday? Depends what we're talking about.)

It is not possible to have just an as². You simply cannot say:

• *The cat is 3 times as the dog.
• *Fred is 3 times as Jack.

It doesn't make any sense; it is ungrammatical. So we can't read the puzzle like that - we must pick a different interpretation.

So:

• The quality being compared is "number of minutes past 10 a.m." - call that $y$
• It is three times something (so $y = 3z$)
• We don't immediately know what it is being compared with. So we don't know $z$; we need to work it out from the context.

Notice that the two clauses in the puzzle are somewhat parallel, in that they share a number of corresponding elements:

This is important, because the parallelism gives a clue to the reader to understand elements in the second half in a similar way to how they were understood in the first half.

In particular, the "many minutes" in both parts gives a clue that this is what is being compared. This makes sense because, since it's what the puzzle's question asks, it is what we're currenly talkign about. In short, $z=y$.

(In fact there is a possibility, though it is less likely given the parallelism, that the puzzle intends you to compare the number of minutes since 10 a.m. as of 68 minutes ago with the number of minutes since 10 a.m. now – but @Rob has shown in his answer that this interpretation is impossible from a mathematical point of view.)

* It is possible to have just an as² in other types of sentence, but not in sentences of the form "X is 3 times as Y".

Other stuff

Here are some other notes on the puzzle that you may find helpful - there are a few other pointers that confirm this interpretation above any other:

The first thing to note is that the question is made up of two main clauses, joined by "if":

• How many minutes is it before 12 noon?
• 68 minutes ago it was three times as many minutes past 10 a.m.

How many minutes is it before 12 noon?

Concentrating on the first clause: this is simple enough, and you have interpreted it correctly (it is asking for $x$ where the current time is $x$ minutes before 12 noon). But do note the following:

• Clue: the verb is "is", which indicates that it is asking about the present. There's no specific word to say "now", but none is needed.
• The subject is "it". This is an impersonal construction; the pronoun "it" doesn't really refer to anything specific: it just refers to the general context. In this case, however, we can replace it with "the time" without changing the meaning.

if

So far a question has been posed (What is $x$?), but we don't have enough information to find it. The "if" signals that the next clause will give further constraints that may allow us to narrow down the answer. It could equally be replaced with "given that".

68 minutes ago

This is adverb phrase indicating the timeframe for the verb. Clue: it indicates that the context for the verb is a specific time in the past - in fact, 68 minutes into the past. Note that this phrase is not the subject of the sentence - though in another context it could be - because it is followed by "it" (the actual subject). Unlike in some languages, English does not allow inserting a subject pronoun that refers to an already-mentioned subject in the same clause (we don't say "*the dog it barked"), so "68 minutes ago" cannot be the subject.

it

As already mentioned, this is the subject. Again, this is an impersonal construction - "it" refers to the context of the verb and (as already established) this means the same as "the time" [at the time of the verb].

was

The verb. Clue: this is past tense, so must be referring to a time in the past. Unlike some languages, for factual "if" clauses such as this, the tense in English is natural - so a past tense implies a reference to the past, whereas in other languages a present tense interpretation is also possible. (Note that things are different for counterfactual "if" clauses.) This is consistent with the fact that, as already mentioned, the timeframe of this verb has been established as "68 minutes ago".

three times as many minutes past 10 a.m.

This is the complement of the verb "was", telling us what the time was in the timeframe of the verb, as a number of minutes past 10 a.m. How many minutes? Let's call that $y$. What is $y$? We don't know exactly, but it is "three times as many minutes". As discussed above, this is an as¹, and a number of things point to the implied object of comparison being $x$. So $y=3x$.