Nerdle #758 Answer
Friday, February 16, 2024
128/8=16
- Structure
- ABC/D=EF
- Type
- Mixed-Length Division
- Result
- 16
How the clues would have read
- Today's equation begins with a two-digit number in the 120s.
- This puzzle uses division only.
- The result is a 2-digit even number.
The numbers behind it
- Divisibility: 128 is divisible by 2, 4, 8, 16, 32, and 64, 8 is divisible by 2 and 4, and 16 is divisible by 2, 4, and 8
- Digital roots: 128 → 1+2+8 = 11 → 2, 8 → 8, 16 → 1+6 = 7
- Prime factorization: 128 = 2⁷, 8 = 2³, 16 = 2⁴
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, 16, factors as 2⁴ — those factors are exactly the operations that could have produced it.
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