June 2018 Fiendish Function

The Fiendish Function posed during June 2018 had the following sample guesses and replies:

  • GUESS
  • REPLY
  • 1
  • 3
  • 2
  • 5
  • 3
  • 9
  • 4
  • 62
  • 5
  • 24
  • 10
  • 4202

The rule was: "Multiply this number of twos together, reverse the order of the digits, then add one".

Suppose the guess was 11:

  • Raise two to this power, giving 2048.
  • Reverse the order of the digits, giving 8402.
  • Add one, giving 8403.

So the result is 8403.