Nerdle #692 Answer
Tuesday, December 12, 2023
43−12=31
- Structure
- AB-CD=EF
- Type
- Double-Digit Subtraction
- Result
- 31
How the clues would have read
- Today's equation begins with a two-digit number in the 40s.
- This puzzle uses subtraction only.
- The result is a 2-digit odd number.
The numbers behind it
- Divisibility: 43 is prime, 12 is divisible by 2, 3, 4, and 6, and 31 is prime
- Digital roots: 43 → 4+3 = 7, 12 → 1+2 = 3, 31 → 3+1 = 4
- Prime factorization: 43 = 43, 12 = 2²×3, 31 = 31
Why the structure matters
This puzzle's shape is AB-CD=EF — a double-digit subtraction, 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 subtraction, most of the search space is gone before you have spent a single guess.
The result, 31, is prime — so it cannot be reached by multiplying two smaller whole numbers, which rules out a whole family of candidate equations immediately.
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