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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?

 

Please email your answers to deputy-director[at]newton.ac[dot]uk and remember to include your name (or the name of the group that you solved the puzzle with) so that we can publish it on our website if you are one of the first few to successfully solve the problem.  

Answers to all puzzles will be published at the end of the month. 

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