Nerdle #684 Answer
Monday, December 4, 2023
112/14=8
- Structure
- ABC/DE=F
- Type
- Mixed-Length Division
- Result
- 8
How the clues would have read
- Today's equation begins with a two-digit number in the 110s.
- This puzzle uses division only.
- The result is a single-digit even number.
The numbers behind it
- Divisibility: 112 is divisible by 2, 4, 7, 8, 14, 16, 28, and 56, 14 is divisible by 2 and 7, and 8 is divisible by 2 and 4
- Digital roots: 112 → 1+1+2 = 4, 14 → 1+4 = 5, 8 → 8
- Prime factorization: 112 = 2⁴×7, 14 = 2×7, 8 = 2³
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, 8, factors as 2³ — those factors are exactly the operations that could have produced it.
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