Harvard-MIT Mathematics Tournament #0ijy
Harvard-MIT Mathematics TournamentHard
From module Expected Value
Community difficultyNo ratings yetBe the first to rate this problem.
Understand the scale
Scale
0.5: Easiest math competition problems, often solvable even for early middle school students without experience.
1: Problems strictly for beginners, often at a moderate middle school level.
1.5: Problems for stronger beginner students, on the level of the middling problems in most middle school contests.
2: For motivated beginners, harder questions from the previous categories.
2.5: More advanced beginner problems, hardest questions from previous categories.
3: Early intermediate problems that require more creative thinking.
3.5: Tougher early intermediate problems that consistently stretch into higher-level creative thinking or conceptual knowledge.
4: Intermediate-level problems.
4.5: Upper intermediate problems approaching the upper bound for non-invitational sprint math competitions.
5: More difficult AIME problems or simple proof-based Olympiad-style problems.
6: High-level AIME-styled questions or introductory Olympiad-level questions.
7: Tougher Olympiad-level questions, may require more technical knowledge.
8: High-level Olympiad-level questions.
9: Expert Olympiad-level questions.
9.5: The hardest problems appearing on Olympiads which the strongest students could reasonably solve.
10: Historically notorious problems, generally unsuitable for even very hard competitions because they are exceedingly tedious, long, and difficult.
Expected valuesPrime numbers
Problem
Problem:
Write down at least one, and up to ten, different 3-digit prime numbers. If you somehow fail to do this, we will ignore your submission for this problem. Otherwise, you're entered into a game with other teams. In this game, you start with 10 points, and each number you write down is like a bet: if no one else writes that number, you gain 1 point, but if anyone else writes that number, you lose 1 point. Thus, your score on this problem can be anything from 0 to 20.