Nerdle #566 Answer
Tuesday, August 8, 2023
49*8=392
- Structure
- AB*C=DEF
- Type
- Mixed-Length Multiplication
- Result
- 392
How the clues would have read
- Today's equation begins with a two-digit number in the 40s.
- This puzzle uses multiplication only.
- The result is a 3-digit even number.
The numbers behind it
- Divisibility: 49 is divisible by 7, 8 is divisible by 2 and 4, and 392 is divisible by 2, 4, 7, 8, 14, 28, 49, 56, 98, and 196
- Digital roots: 49 → 4+9 = 13 → 4, 8 → 8, 392 → 3+9+2 = 14 → 5
- Prime factorization: 49 = 7², 8 = 2³, 392 = 2³×7²
Why the structure matters
This puzzle's shape is AB*C=DEF — a mixed-length multiplication, 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 multiplication, most of the search space is gone before you have spent a single guess.
The result, 392, factors as 2³×7² — those factors are exactly the operations that could have produced it.
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