January 2016 Fiendish Function

The Fiendish Function posed during January 2016 had the following sample guesses and replies:

  • GUESS
  • REPLY
  • 1
  • 0
  • 2
  • 7
  • 3
  • 11
  • 4
  • 14
  • 5
  • 101
  • 10
  • 108

The rule was: "Write the number in binary, then add the prime factors together".

Suppose the guess was 22:

  • Write the number in binary, giving 10110.
  • Factorise the number into prime factors, giving 337, 5, 3, 2
  • Add these together, giving 347.

So the result is 347.