Yesterday, I played until late at night too much. [Syntax]

The correct answer is まで. The sentence means 'Yesterday, I played until late at night too much.' The particle まで indicates the extent or limit of an action, here specifying 'until late at night' (夜遅くまで). It connects the time phrase 'late at night' to the action of playing. The phrase 遊(あそ)びすぎました means 'played too much' (verb stem + すぎる). Therefore, まで logically completes the phrase '夜遅くまで' (until late at night). '夜' means night, '遅く' means late (adverb), and '遊び' is the verb stem, none of which fit this specific grammatical slot.

正解は「まで」です。「まで」は動作の及ぶ範囲や期限を示します。「夜遅くまで」で「夜遅い時間まで」という意味になります。「遊びすぎました」の前に来る助詞として「まで」が適切です。「夜」「遅く」「遊び」は文法的に不自然です。