A home-schooled student writes a program to generate 5-digit positive integers where each digit is either 3 or 7. What is the probability that such a number contains at least two consecutive 3s?

Thu, 30 Apr 2026 10:21:40 +0000

**A home-schooled student writes a program to generate 5-digit positive integers where each digit is either 3 or 7. What is the probability that such a number contains at least two consecutive 3s?** In an age where young coders worldwide explore logic, patterns, and probabilities, one curious student crafted a simple program to generate 5-digit numbers using only the digits 3 and 7. With no explicit intent beyond understanding sequences, this small project has quietly sparked broader interest in how chance shapes patterns—even in artificial numbers. As more people explore computational thinking, questions about predictable sequences gain real-world relevance. This pattern search centers on a deceptively simple question: What’s the chance that a randomly chosen 5-digit number made only of 3s and 7s contains at least two adjacent 3s? Unlike purely random combinations, these constraints shape every possibility—offering a clear mathematical framework to explore patterns hidden in structured randomness. ---