May 2018 Fiendish Function

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

• GUESS
• REPLY
• 1
• 1
• 2
• 6
• 3
• 7
• 4
• 52
• 5
• 53
• 10
• 510

The rule was: "Write the number in binary, add the original number, then divide it by two (ignoring the remainder)".

Suppose the guess was 22:

• Write the number in binary, giving 10110.
• Add the original number, giving 10132.
• Divide it by two (ignoring the remainder), giving 5066.

So the result is 5066.