Par iactus certamen mutat.

• par: an adjective, nominative singular, meaning equal, matching, or even
• iactus: a noun, nominative singular, meaning throw, cast, or toss
• certamen: a noun, accusative singular, meaning contest, competition, or struggle
• mutat: a verb, 3rd person singular present active, meaning changes

So the sentence structure is:

subject = par iactus
object = certamen
verb = mutat

In other words, an equal throw changes the contest.

Because par and iactus go together as a nominative singular phrase.

• par is nominative singular here.
• iactus is also nominative singular.
• mutat is singular, so it needs a singular subject.

Meanwhile, certamen is a neuter noun whose nominative and accusative singular look the same. In this sentence, it makes best sense as the direct object of mutat.

So Latin is telling us:

par iactus = the thing doing the action
certamen = the thing being changed

Here it means equal or matching, not a pair.

That is because par is being used as an adjective modifying iactus. It agrees with iactus in case and number and describes what kind of throw it is.

If Latin wanted to say something more like a pair of throws, the construction would normally look different.

Because the dictionary form of the adjective is par, paris.

That means:

• par = nominative singular
• paris = genitive singular

So par is exactly the form we expect when it agrees with a nominative singular noun such as iactus.

If it were accusative masculine singular, it would be parem. But iactus is not accusative here, so parem would not fit.

Here it is a noun meaning throw or cast.

That is worth noticing because iactus can also be a participial form in other contexts. But in this sentence, it works as a noun because:

• it is modified by par
• it serves as the subject of mutat
• the sentence makes good sense with the noun meaning throw

So here you should read par iactus as an equal throw, not as a participial phrase.

mutat is:

• present tense
• active voice
• indicative mood
• 3rd person singular

It comes from muto, mutare, meaning to change.

So mutat means he/she/it changes or sometimes is changing.
Since the subject is par iactus, the most natural English is changes.

Because the verb mutat is transitive: it normally takes a direct object, something that gets changed.

Also, the sentence already has a clear nominative subject phrase: par iactus.

So although certamen could theoretically be either nominative or accusative in form, syntax tells us it is accusative here:

• par iactus = subject
• certamen = object

This is very common with neuter third-declension nouns, since nominative and accusative singular are identical in form.

Latin word order is much freer than English word order because Latin uses endings, not position alone, to show grammatical function.

English strongly prefers:

subject + verb + object

But Latin often prefers:

subject + object + verb

So:

Par iactus certamen mutat

is perfectly normal Latin. A very literal order would be:

Equal throw contest changes

But you should not translate Latin by position alone. You translate by case endings and verb forms.

Because Latin has no articles.

So par iactus can mean:

• an equal throw
• the equal throw

And certamen can mean:

• a contest
• the contest

Context decides which English article is best. Latin leaves that unstated unless something else makes it clear.

iactus is actually a fourth-declension noun.

Its basic forms are:

• nominative singular: iactus
• genitive singular: iactūs
• accusative singular: iactum

So even though -us often makes English-speaking learners think of the second declension, not every -us noun is second declension. iactus is a good example of that.