Nerdle #821 Answer
Friday, April 19, 2024
60*9=540
- Structure
- AB*C=DEF
- Type
- Mixed-Length Multiplication
- Result
- 540
How the clues would have read
- Today's equation begins with a two-digit number in the 60s.
- This puzzle uses multiplication only.
- The result is a 3-digit even number.
The numbers behind it
- Divisibility: 60 is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30, 9 is divisible by 3, and 540 is divisible by 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, and 270
- Digital roots: 60 → 6+0 = 6, 9 → 9, 540 → 5+4+0 = 9
- Prime factorization: 60 = 2²×3×5, 9 = 3², 540 = 2²×3³×5
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, 540, factors as 2²×3³×5 — those factors are exactly the operations that could have produced it.
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