In die festo pueri minus laborant, sed coquus tota die in culina occupatus est.

Die festo is ablative singular.

• die is the ablative singular of dies (day)
• festo is the ablative singular of festus (festive, holiday) and agrees with die

So in die festo means on a holiday or on a festival day.

The preposition in here takes the ablative because it is expressing a time setting, not motion.

Yes. A learner may often see time expressions without a preposition in Latin.

Classical Latin commonly uses the ablative of time when by itself:

• die festo = on a holiday

So in die festo is understandable and perfectly clear, but die festo is often what students are taught as the more typical classical way.

Because festo has to agree with die.

The noun dies is here in the ablative singular (die), so the adjective festus must also be ablative singular:

• dies festus = a holiday / festival day
• in die festo = on a holiday

This is normal Latin adjective agreement: adjectives agree with their nouns in case, number, and gender.

Here pueri is nominative plural, so it is the subject of laborant.

We know it means the boys because:

• laborant is 3rd person plural = they work
• so the subject must be plural
• pueri fits that perfectly as the boys

A beginner may notice that pueri can also be genitive singular (of the boy), but that reading does not fit with laborant.

Minus is a comparative adverb, meaning less.

So:

• laborant = they work
• minus laborant = they work less

It modifies the verb, not a noun.

This is like English less in they work less.

Latin often leaves that unstated if the comparison is general or obvious from context.

So minus laborant simply means:

• they work less
• or they do less work

It does not have to say than usual or than on other days, even though that is probably the idea.

If Latin wanted to say less than..., it could make the comparison explicit, but here it is left understood.

Coquus is nominative singular, because it is the subject of est.

So the second clause is:

• sed coquus ... occupatus est
• but the cook ... is busy / occupied

The sentence contrasts two subjects:

• pueri = the boys
• coquus = the cook

Because occupatus is functioning like an adjective, and est means is.

So:

• occupatus = occupied, busy
• est = is
• occupatus est = is occupied / is busy

This is very common in Latin: an adjective or participle is combined with a form of sum (to be).

In this sentence, the meaning is really more like is busy than a literal passive has been occupied.

Because it agrees with coquus.

• coquus = nominative singular masculine
• occupatus = nominative singular masculine

Latin adjectives and participles must agree with the noun they describe. Since the cook is one masculine person, occupatus must be masculine singular too.

Tota die means the whole day or all day.

• tota = whole, entire
• die = day in the ablative singular

So literally it is something like throughout the whole day.

A learner may expect totam diem, since the accusative is very common for duration of time. That is a useful instinct. But tota die is also used to express the time span here as throughout the day / all day.

Because in with the ablative shows location:

• in culina = in the kitchen

Latin uses:

• in + ablative for in/on a place
• in + accusative for motion into a place

So:

• in culina = in the kitchen
• in culinam = into the kitchen

Because Latin word order is flexible, and the verb often comes late in the clause.

English depends more on word order, but Latin depends more on endings. That lets Latin move words around for emphasis or style.

So:

• sed coquus tota die in culina occupatus est

is completely natural Latin word order. The important information is saved until the end: is busy.

Sed means but and marks a contrast.

The contrast is:

• the boys work less
• but the cook is busy all day in the kitchen

So sed shows that the second idea goes against what you might expect from the first.

Yes, here dies is masculine.

That is why the adjective is:

• festo in die festo
• not a feminine form

A student may hear that dies can sometimes be feminine, and that is true in some contexts, but it is usually masculine, especially in ordinary expressions like this one.

This is just normal Latin flexibility.

Latin often arranges words by emphasis rather than by a fixed English-style pattern. In this sentence:

• pueri comes early so we know who the first clause is about
• minus is placed near laborant because it modifies it
• occupatus est comes at the end, giving the second clause a neat finish

So the sentence is not unusual; it is a good example of Latin’s freer word order.