Nerdle #638 Answer
Thursday, October 19, 2023
8*70=560
- Structure
- A*BC=DEF
- Type
- Mixed-Length Multiplication
- Result
- 560
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 even number.
The numbers behind it
- Divisibility: 8 is divisible by 2 and 4, 70 is divisible by 2, 5, 7, 10, 14, and 35, and 560 is divisible by 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, and 280
- Digital roots: 8 → 8, 70 → 7+0 = 7, 560 → 5+6+0 = 11 → 2
- Prime factorization: 8 = 2³, 70 = 2×5×7, 560 = 2⁴×5×7
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, 560, factors as 2⁴×5×7 — those factors are exactly the operations that could have produced it.
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