In this way, the game came to ____ end.

CONCEPT: The indefinite article in English has two spoken forms — "a" and "an" — chosen by the SOUND that opens the very next word, not its spelling: "a" precedes a word that opens with a consonant sound, and "an" precedes a word that opens with a vowel sound. The definite article "the" is reserved for a noun already identified or made specific by context, and a singular countable noun in English almost never appears with no article at all.

APPLICATION: In "In this way, the game came to ____ end," the blank sits directly before the singular countable noun "end," and "end" opens with the vowel sound /e/. Nothing earlier in the sentence points to one particular, already-known "end," so the definite article does not apply here, and dropping the article altogether is not possible for a singular countable noun like "end." That leaves only the choice between the two indefinite-article forms, which the initial vowel sound of "end" resolves directly.

CROSS-CHECK — why the other forms don't fit:

• "the" needs a specific, previously-established "end" in context — this sentence introduces the completion for the first time, so nothing licenses the definite article.

• "a" pairs with a following consonant sound, so whether it fits depends on how "end" is actually pronounced at its start — check that sound rather than assuming this form.

• "No article is needed" would only work for an uncountable or general plural noun — "end" here is singular and countable, so some article is required.

• The fixed collocation "come to an end" (meaning to finish/conclude) is the idiomatic form that satisfies every one of these checks at once.

Result: the sentence takes the indefinite article before the vowel sound — "came to an end."