Nerdle #112 Answer
Wednesday, May 11, 2022
357/7=51
- Structure
- ABC/D=EF
- Type
- Mixed-Length Division
- Result
- 51
How the clues would have read
- Today's equation begins with a two-digit number in the 350s.
- This puzzle uses division only.
- The result is a 2-digit odd number.
The numbers behind it
- Divisibility: 357 is divisible by 3, 7, 17, 21, 51, and 119, 7 is prime, and 51 is divisible by 3 and 17
- Digital roots: 357 → 3+5+7 = 15 → 6, 7 → 7, 51 → 5+1 = 6
- Prime factorization: 357 = 3×7×17, 7 = 7, 51 = 3×17
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, 51, factors as 3×17 — those factors are exactly the operations that could have produced it.
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