Nerdle #395 Answer
Saturday, February 18, 2023
340/68=5
- Structure
- ABC/DE=F
- Type
- Mixed-Length Division
- Result
- 5
How the clues would have read
- Today's equation begins with a two-digit number in the 340s.
- This puzzle uses division only.
- The result is a single-digit odd number.
The numbers behind it
- Divisibility: 340 is divisible by 2, 4, 5, 10, 17, 20, 34, 68, 85, and 170, 68 is divisible by 2, 4, 17, and 34, and 5 is prime
- Digital roots: 340 → 3+4+0 = 7, 68 → 6+8 = 14 → 5, 5 → 5
- Prime factorization: 340 = 2²×5×17, 68 = 2²×17, 5 = 5
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, 5, 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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