Nerdle #181 Answer
Tuesday, July 19, 2022
56+28=84
- Structure
- AB+CD=EF
- Type
- Double-Digit Addition
- Result
- 84
How the clues would have read
- Today's equation begins with a two-digit number in the 50s.
- This puzzle uses addition only.
- The result is a 2-digit even number.
The numbers behind it
- Divisibility: 56 is divisible by 2, 4, 7, 8, 14, and 28, 28 is divisible by 2, 4, 7, and 14, and 84 is divisible by 2, 3, 4, 6, 7, 12, 14, 21, 28, and 42
- Digital roots: 56 → 5+6 = 11 → 2, 28 → 2+8 = 10 → 1, 84 → 8+4 = 12 → 3
- Prime factorization: 56 = 2³×7, 28 = 2²×7, 84 = 2²×3×7
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, 84, factors as 2²×3×7 — those factors are exactly the operations that could have produced it.
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