Nerdle #192 Answer
Saturday, July 30, 2022
40+42=82
- Structure
- AB+CD=EF
- Type
- Double-Digit Addition
- Result
- 82
How the clues would have read
- Today's equation begins with a two-digit number in the 40s.
- This puzzle uses addition only.
- The result is a 2-digit even number.
The numbers behind it
- Divisibility: 40 is divisible by 2, 4, 5, 8, 10, and 20, 42 is divisible by 2, 3, 6, 7, 14, and 21, and 82 is divisible by 2 and 41
- Digital roots: 40 → 4+0 = 4, 42 → 4+2 = 6, 82 → 8+2 = 10 → 1
- Prime factorization: 40 = 2³×5, 42 = 2×3×7, 82 = 2×41
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, 82, factors as 2×41 — those factors are exactly the operations that could have produced it.
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