Nerdle #381 Answer
Saturday, February 4, 2023
7*77=539
- Structure
- A*BC=DEF
- Type
- Mixed-Length Multiplication
- Result
- 539
How the clues would have read
- Today's equation begins with a single-digit number.
- This puzzle uses multiplication only.
- The result is a 3-digit odd number.
The numbers behind it
- Divisibility: 7 is prime, 77 is divisible by 7 and 11, and 539 is divisible by 7, 11, 49, and 77
- Digital roots: 7 → 7, 77 → 7+7 = 14 → 5, 539 → 5+3+9 = 17 → 8
- Prime factorization: 7 = 7, 77 = 7×11, 539 = 7²×11
Why the structure matters
This puzzle's shape is A*BC=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, 539, factors as 7²×11 — those factors are exactly the operations that could have produced it.
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