nerdle

Nerdle #814 Answer

Friday, April 12, 2024

20*1/5=4
Structure
AB*C/D=E
Type
Mixed Multiplication and Division
Result
4

How the clues would have read

  • Today's equation begins with a two-digit number in the 20s.
  • This puzzle uses division and multiplication operations.
  • The result is a single-digit even number.

The numbers behind it

  • Divisibility: 20 is divisible by 2, 4, 5, and 10, 1 is prime, 5 is prime, and 4 is divisible by 2
  • Digital roots: 20 → 2+0 = 2, 1 → 1, 5 → 5, 4 → 4
  • Prime factorization: 20 = 2²×5, 1 has no prime factors, 5 = 5, 4 = 2²

Why the structure matters

This puzzle's shape is AB*C/D=E — a mixed multiplication and division, 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 multiplication and division, most of the search space is gone before you have spent a single guess.

The result, 4, factors as 2² — those factors are exactly the operations that could have produced it.

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