2023 AIME I Problems

2023 AIME I (Answer Key) | AoPS Contest Collections • PDF

Instructions This is a 15-question, 3-hour examination. All answers are integers ranging from to , inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers. No aids other than scratch paper, graph paper, ruler, compass, and protractor are permitted. In particular, calculators and computers are not permitted.

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Problem 1

Let n be a positive integer such that 1 ≤ n ≤ 1000 . Let be the number of integers in the set = { ,, . . . , } .

Let a = max{ : 1 ≤ n ≤ 1000}, and b = min{ : 1 ≤ n ≤ 1000}. Find a − b .

Solution

Problem 2

Find the number of elements in the set

{ ∈  : 2 ≤ ≤ 2023, }

Solution