## Instruction
Inspired by the provided math content, craft a math problem suitable for the AMC 8 competition, engaging top grade students with a challenge in areas of arithmetic, algebra, counting, geometry, logic, number theory, or probability. Ensure the problem stimulates problem-solving techniques and heuristics within a text-based and solvable format, avoiding advanced subjects like calculus or physics.

## Math Content
<EXTRACT>

## Guidelines
[Problem]: Design a compelling, self-contained math problem for AMC 8 contestants inspired by the math content, incorporating elements of basic math disciplines. The problem should be approachable through logical reasoning and fundamental problem-solving strategies. Ensure the problem is fully text-based, solvable without the aid of images, and has a difficulty level appropriate for the AMC 8 competition.

[Solution]: Provide a detailed, step-by-step solution that is educational and tailored to the AMC 8 audience, around 250-350 words long. Explain the logic and reasoning behind each step thoroughly, using clear and age-appropriate language and terminology to facilitate understanding. Highlight the use of problem-solving techniques and heuristics employed in the solution.

## New Problem