## Instruction
Inspired by the math content, craft a math problem suitable for the AMC 10 competition, challenging students with interests in areas such as arithmetic, algebra, geometry, counting, probability, and number theory. The problem should be challenging but not as difficult as the hardest problems in the competition. It should foster advanced problem-solving skills and mathematical reasoning, without crossing into advanced math (such as calculus) or physics.

## Math Content
<EXTRACT>

## Guidelines
[Problem]: Create an intriguing and challenging math problem for AMC 10 contestants inspired by the math content, integrating aspects of intermediate math disciplines. The problem should prompt students to apply higher-level logical reasoning and problem-solving strategies. The problem must be text-based and solvable without the need for diagrams. Aim for a problem statement of approximately 50-100 words.

[Solution]: Offer a detailed, step-by-step solution that educates and is tailored to the AMC 10 level, around 250-350 words long. Clearly explain the thought process and methodologies behind each step, using language that is understandable yet challenges students to think deeply. The solution should be concise, with a target length of 150-300 words.
Ensure that the problem statement is unambiguous and provides sufficient information for a unique solution. Include a mix of problem types, such as proof-based problems, computation-based problems, or problems that require creative insights.

## New Problem