Nerdle #347 Answer
Sunday, January 1, 2023
147/49=3
- Structure
- ABC/DE=F
- Type
- Mixed-Length Division
- Result
- 3
How the clues would have read
- Today's equation begins with a two-digit number in the 140s.
- This puzzle uses division only.
- The result is a single-digit odd number.
The numbers behind it
- Divisibility: 147 is divisible by 3, 7, 21, and 49, 49 is divisible by 7, and 3 is prime
- Digital roots: 147 → 1+4+7 = 12 → 3, 49 → 4+9 = 13 → 4, 3 → 3
- Prime factorization: 147 = 3×7², 49 = 7², 3 = 3
Why the structure matters
This puzzle's shape is ABC/DE=F — a mixed-length division, where each letter stands for one digit. Recognising the shape before the arithmetic is what separates a three-guess solve from a six-guess struggle: once you know the equation is a mixed-length division, most of the search space is gone before you have spent a single guess.
The result, 3, is prime — so it cannot be reached by multiplying two smaller whole numbers, which rules out a whole family of candidate equations immediately.
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