Nerdle #538 Answer
Tuesday, July 11, 2023
84*8=672
- Structure
- AB*C=DEF
- Type
- Mixed-Length Multiplication
- Result
- 672
How the clues would have read
- Today's equation begins with a two-digit number in the 80s.
- This puzzle uses multiplication only.
- The result is a 3-digit even number.
The numbers behind it
- Divisibility: 84 is divisible by 2, 3, 4, 6, 7, 12, 14, 21, 28, and 42, 8 is divisible by 2 and 4, and 672 is divisible by 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, and 336
- Digital roots: 84 → 8+4 = 12 → 3, 8 → 8, 672 → 6+7+2 = 15 → 6
- Prime factorization: 84 = 2²×3×7, 8 = 2³, 672 = 2⁵×3×7
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, 672, factors as 2⁵×3×7 — those factors are exactly the operations that could have produced it.
Nerdle is made by Nerdle Limited. nerdle.vip is an independent fan site and is not affiliated with or endorsed by them. Puzzle numbers and answers on this page refer to the official game at nerdlegame.com.