Nerdle #585 Answer
Sunday, August 27, 2023
31+47=78
- Structure
- AB+CD=EF
- Type
- Double-Digit Addition
- Result
- 78
How the clues would have read
- Today's equation begins with a two-digit number in the 30s.
- This puzzle uses addition only.
- The result is a 2-digit even number.
The numbers behind it
- Divisibility: 31 is prime, 47 is prime, and 78 is divisible by 2, 3, 6, 13, 26, and 39
- Digital roots: 31 → 3+1 = 4, 47 → 4+7 = 11 → 2, 78 → 7+8 = 15 → 6
- Prime factorization: 31 = 31, 47 = 47, 78 = 2×3×13
Why the structure matters
This puzzle's shape is AB+CD=EF — a double-digit addition, 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 double-digit addition, most of the search space is gone before you have spent a single guess.
The result, 78, factors as 2×3×13 — those factors are exactly the operations that could have produced it.
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