Nerdle #705 Answer
Monday, December 25, 2023
186/62=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 180s.
- This puzzle uses division only.
- The result is a single-digit odd number.
The numbers behind it
- Divisibility: 186 is divisible by 2, 3, 6, 31, 62, and 93, 62 is divisible by 2 and 31, and 3 is prime
- Digital roots: 186 → 1+8+6 = 15 → 6, 62 → 6+2 = 8, 3 → 3
- Prime factorization: 186 = 2×3×31, 62 = 2×31, 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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