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Challenge 352: Composite Combinations

Some positive even integers can be written as the sum of two positive odd numbers, both of which are composite (this means "not prime and not equal to 1"). For example, 36 = 9 + 27 ( or 15 + 21)

We will call positive even integers with this property silverback numbers. So 36 is a silverback number.

  • How many positive even integers less than or equal to 40 are not silverback numbers?
  • How many positive even integers greater than 40 are not silverback numbers?

Provide the best evidence you can for your answers.

Submit your solution

Please do send in your solution to this problem to  weeklymaths@kcl.ac.uk  You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.

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