August 2017 Fiendish Function

The Fiendish Function posed during August 2017 had the following sample guesses and replies:

  • GUESS
  • REPLY
  • 1
  • 2
  • 2
  • 12
  • 3
  • 14
  • 4
  • 104
  • 5
  • 106
  • 10
  • 1020

The rule was: "Write the number in binary, then add the original number".

Suppose the guess was 19:

  • Write the number in binary, giving 10011.
  • Add the original number, giving 10030.

So the result is 10030.