Numerus impar adversario placet, et ille lusorem provocat.

Because placeo, placere works differently from English to please.

In Latin, the thing that is pleasing is the subject, and the person who likes it is put in the dative:

• Numerus impar = the odd number
• adversario placet = is pleasing to the opponent

So Latin is really saying:

• The odd number is pleasing to the opponent

rather than using the English-style pattern the opponent likes the odd number.

The subject is numerus impar.

You can tell because:

• numerus is nominative singular
• impar agrees with numerus
• placet is third person singular, so it matches a singular subject

So:

• Numerus impar placet = The odd number pleases / is pleasing

The person receiving that feeling, adversario, is not the subject.

Impar is an adjective modifying numerus.

They agree in:

• case: nominative
• number: singular
• gender: masculine

So numerus impar means an odd number or the odd number.

A useful point: impar is a third-declension adjective, so it does not look like a first/second-declension adjective such as bonus, bona, bonum. Even so, it still agrees normally with the noun it modifies.

Because that is how the Latin verb placeo is constructed.

Compare:

• English: The opponent likes the odd number
• Latin-style logic: The odd number pleases the opponent

So in Latin:

• numerus impar adversario placet

literally follows the second pattern.

This is very common in Latin and worth getting used to. Other verbs also use cases in ways that do not line up neatly with English.

It can mean either, depending on context.

Originally, ille is a demonstrative meaning that. But very often it is also used like a pronoun:

• that man
• he
• sometimes the former mentioned person

In this sentence, ille most naturally refers to adversario from the first clause, so the sense is:

• and he challenges the player

Using ille can give a slightly more pointed or emphatic feel than a very plain pronoun.

Because the two words do not have to be in the same case to refer to the same person.

In the first clause, the opponent appears as:

• adversario = to the opponent (dative)

In the second clause, that same person becomes the subject:

• ille = he / that man (nominative)

So the person is the same, but his grammatical role changes from one clause to the next.

Because lusorem is the direct object of provocat.

• provocat = he challenges
• the person challenged is the direct object
• therefore Latin uses the accusative

So:

• ille lusorem provocat = he challenges the player

lusorem is the accusative singular of lusor.

It is related, but in this sentence challenges is probably the best sense.

The verb provoco, provocare can mean things like:

• call out
• challenge
• provoke

In a competitive or game-like context, challenge is usually the most natural translation. So ille lusorem provocat is not necessarily saying that he annoys the player; it is more likely saying that he issues a challenge.

Because Latin word order is much more flexible than English word order.

English depends heavily on position:

• subject + verb + object

Latin depends much more on endings, so writers can move words around for emphasis, style, or rhythm.

In this sentence:

• Numerus impar comes first, giving prominence to the odd number
• adversario appears before placet, which is a very normal placement for the dative with this verb
• ille begins the second clause after et, clearly marking the new subject

A more English-like order would still mean the same thing if the endings stayed the same.

Both are:

• present tense
• active voice
• indicative mood
• third person singular

So:

• placet = he/she/it pleases or is pleasing
• provocat = he/she/it challenges

Their singular form matches their singular subjects:

• numerus impar placet
• ille provocat

Because Latin has no definite or indefinite articles.

So a noun like numerus can mean:

• a number
• the number

and lusorem can mean:

• a player
• the player

The context tells you which is more natural in translation.

That is why one Latin sentence can often be translated into English in more than one acceptable way.