Nerdle #135 Answer
Friday, June 3, 2022
96+9=105
- Structure
- AB+C=DEF
- Type
- Mixed-Length Addition
- Result
- 105
How the clues would have read
- Today's equation begins with a two-digit number in the 90s.
- This puzzle uses addition only.
- The result is a 3-digit odd number.
The numbers behind it
- Divisibility: 96 is divisible by 2, 3, 4, 6, 8, 12, 16, 24, 32, and 48, 9 is divisible by 3, and 105 is divisible by 3, 5, 7, 15, 21, and 35
- Digital roots: 96 → 9+6 = 15 → 6, 9 → 9, 105 → 1+0+5 = 6
- Prime factorization: 96 = 2⁵×3, 9 = 3², 105 = 3×5×7
Why the structure matters
This puzzle's shape is AB+C=DEF — a mixed-length 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 mixed-length addition, most of the search space is gone before you have spent a single guess.
The result, 105, factors as 3×5×7 — those factors are exactly the operations that could have produced it.
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