Question: How many distinct 7-digit positive integers can be formed using only the digits 1, 3, and 5, such that no two adjacent digits are the same?

Sun, 03 May 2026 16:10:06 +0000

**Discover Hook: Why the numbers made of 1, 3, and 5 are more than just a math puzzle**
In a world where patterns drive everything from algorithms to financial trends, a simple mathematical question quietly intrigues curious minds: how many unique 7-digit numbers can be formed using only the digits 1, 3, and 5—without repeating the same digit consecutively? This isn’t just a classroom riddle—it’s a gateway into combinatorics, digital literacy, and the hidden structure behind seemingly random sequences. For users browsing on mobile devices through Discover, this query reflects a growing curiosity about patterns, order, and the logic shaping modern digital experiences. **Why This Question Is Gaining Traction Across the US**
Across the United States, audiences are increasingly drawn to questions blending logic, math, and real-world relevance—especially in the mobile-first era where digestible insights fuel engagement. This particular problem captures attention because it’s accessible yet intellectually satisfying, aligning with trends in ed-tech, personal development, and trend analysis. Platforms and search behavior show growing interest in pattern recognition, digital creativity, and foundational math skills—key themes shaping user search intent. **How Many Valid 7-Digit Sequences Exist with 1, 3, and 5?**
Each digit in a valid 7-digit number must be 1, 3, or 5, with the strict rule that no two adjacent digits can be the same. This constraint creates a structured branching process: for the first digit, all three choices (1, 3, 5) are valid; but each subsequent digit must differ from the prior one, leaving only two options. Mathematically, this forms a pattern:
- First digit: 3 choices
- Each next digit (positions 2 through 7): 2 choices, since each must differ from the previous