Nerdle #923 Answer
Tuesday, July 30, 2024
252/9=28
- Structure
- ABC/D=EF
- Type
- Mixed-Length Division
- Result
- 28
How the clues would have read
- Today's equation begins with a two-digit number in the 250s.
- This puzzle uses division only.
- The result is a 2-digit even number.
The numbers behind it
- Divisibility: 252 is divisible by 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, and 126, 9 is divisible by 3, and 28 is divisible by 2, 4, 7, and 14
- Digital roots: 252 → 2+5+2 = 9, 9 → 9, 28 → 2+8 = 10 → 1
- Prime factorization: 252 = 2²×3²×7, 9 = 3², 28 = 2²×7
Why the structure matters
This puzzle's shape is ABC/D=EF — 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, 28, factors as 2²×7 — those factors are exactly the operations that could have produced it.
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