Nerdle #205 Answer
Friday, August 12, 2022
50*3=150
- Structure
- AB*C=DEF
- Type
- Mixed-Length Multiplication
- Result
- 150
How the clues would have read
- Today's equation begins with a two-digit number in the 50s.
- This puzzle uses multiplication only.
- The result is a 3-digit even number.
The numbers behind it
- Divisibility: 50 is divisible by 2, 5, 10, and 25, 3 is prime, and 150 is divisible by 2, 3, 5, 6, 10, 15, 25, 30, 50, and 75
- Digital roots: 50 → 5+0 = 5, 3 → 3, 150 → 1+5+0 = 6
- Prime factorization: 50 = 2×5², 3 = 3, 150 = 2×3×5²
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, 150, factors as 2×3×5² — those factors are exactly the operations that could have produced it.
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