Nerdle #466 Answer
Sunday, April 30, 2023
180/30=6
- Structure
- ABC/DE=F
- Type
- Mixed-Length Division
- Result
- 6
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 even number.
The numbers behind it
- Divisibility: 180 is divisible by 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, and 90, 30 is divisible by 2, 3, 5, 6, 10, and 15, and 6 is divisible by 2 and 3
- Digital roots: 180 → 1+8+0 = 9, 30 → 3+0 = 3, 6 → 6
- Prime factorization: 180 = 2²×3²×5, 30 = 2×3×5, 6 = 2×3
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, 6, factors as 2×3 — those factors are exactly the operations that could have produced it.
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