Nerdle #271 Answer
Monday, October 17, 2022
- Structure
- AB-C*D=E
- Type
- Mixed Subtraction and Multiplication
- Result
- 3
How the clues would have read
- Today's equation begins with a two-digit number in the 40s.
- This puzzle uses multiplication and subtraction operations.
- The result is a single-digit odd number.
The numbers behind it
- Divisibility: 45 is divisible by 3, 5, 9, and 15, 7 is prime, 6 is divisible by 2 and 3, and 3 is prime
- Digital roots: 45 → 4+5 = 9, 7 → 7, 6 → 6, 3 → 3
- Prime factorization: 45 = 3²×5, 7 = 7, 6 = 2×3, 3 = 3
Why the structure matters
This puzzle's shape is AB-C*D=E — a mixed subtraction and 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 subtraction and multiplication, most of the search space is gone before you have spent a single guess.
The result, 3, is prime — so it cannot be reached by multiplying two smaller whole numbers, which rules out a whole family of candidate equations immediately.
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