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Summer Maths Puzzles - Wednesday 21 August - Consecutive Numbers

Consecutive Numbers

How many numbers from 1 up to 2019 can be expressed as

  1. The sum of 4 consecutive whole numbers?
  2. The product of 4 consecutive whole numbers?

Bonus question: by considering multiples of 4 or otherwise, can you prove that no number is both the sum and product of 4 consecutive whole numbers?

 

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons