December 2018 Fiendish Function

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

  • GUESS
  • REPLY
  • 1
  • 1
  • 2
  • 4
  • 3
  • 100
  • 4
  • 121
  • 5
  • 144
  • 10
  • 10201

The rule was: "Write the number in base three, then square it".

Suppose the guess was 22:

  • Write the number in base three, giving 211.
  • Multiply the number by itself, giving 44521.

So the result is 44521.