Nerdle #121 Answer
Friday, May 20, 2022
99*4=396
- Structure
- AB*C=DEF
- Type
- Mixed-Length Multiplication
- Result
- 396
How the clues would have read
- Today's equation begins with a two-digit number in the 90s.
- This puzzle uses multiplication only.
- The result is a 3-digit even number.
The numbers behind it
- Divisibility: 99 is divisible by 3, 9, 11, and 33, 4 is divisible by 2, and 396 is divisible by 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, and 198
- Digital roots: 99 → 9+9 = 18 → 9, 4 → 4, 396 → 3+9+6 = 18 → 9
- Prime factorization: 99 = 3²×11, 4 = 2², 396 = 2²×3²×11
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, 396, factors as 2²×3²×11 — those factors are exactly the operations that could have produced it.
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