Nerdle #360 Answer
Saturday, January 14, 2023
308/44=7
- Structure
- ABC/DE=F
- Type
- Mixed-Length Division
- Result
- 7
How the clues would have read
- Today's equation begins with a two-digit number in the 300s.
- This puzzle uses division only.
- The result is a single-digit odd number.
The numbers behind it
- Divisibility: 308 is divisible by 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154, 44 is divisible by 2, 4, 11, and 22, and 7 is prime
- Digital roots: 308 → 3+0+8 = 11 → 2, 44 → 4+4 = 8, 7 → 7
- Prime factorization: 308 = 2²×7×11, 44 = 2²×11, 7 = 7
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, 7, 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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