The AI Mathematical Olympiad (AIMO) is a competition aimed at developing algorithms and models capable of solving complex math problems. Recent events include AI systems achieving silver-medal standards in the International Mathematical Olympiad and the awarding of progress prizes to teams like Numina for their innovative solutions.
(https://www.kaggle.com/competitions/ai-mathematical-olympiad-progress-prize-2)
Overview: Briefly introduce the purpose of the document. Problem List: A numbered summary of the problems. Solutions: Each problem's solution with proper formatting, using LaTeX or code blocks for equations. Citation: Include the competition citation and references.
- Flight Scheduling: Find the longest consecutive days without flights given varying schedules.
- Triangle Geometry: Solve for the segment length based on bisectors and circumcircles.
- Perpendicular Height: Maximize the altitude of a triangle with specific conditions.
- Three-Digit Number Puzzle: Determine divisors for large constructed numbers.
- Erased Numbers: Calculate the sum of erased numbers and their modular impact.
- Artificial Numbers: Explore integers satisfying specific GCD conditions.
- Delightful Sequences: Identify sequences with unique combinatorial properties.
- Tennis Pairing: Count arrangements avoiding a specific pairing.
- Digit Sums: Analyze sums of digits in large numerical sequences. 10.Fibonacci and Primes: Evaluate Fibonacci properties and find prime factors.
Problem: Determine the longest run of consecutive days without any flights given three airlines' schedules.
Answer: 79 days.
Problem: Solve for the segment length using bisectors and circumcircles.
Answer: ( m+n = 751 ).
For more details about the competition and citation information, refer to the official Kaggle competition page: AIMO Progress Prize 2 on Kaggle