What is the largest number $ x $ such that $ x_{16}, $ i.e. $ x $ in base 16, is a 5-digit long palindrome, where each digit appears at most twice? A palindrome is a number that reads the same forward as it does backward, such as 737 or 24542.

  • $\begingroup$ Welcome to Puzzling! Is this a puzzle you created yourself? If not, please edit in a source (such as a link). We have an attribution policy, and unsourced puzzles will be closed and perhaps deleted. $\endgroup$
    – bobble
    Mar 22 '21 at 23:52
  • $\begingroup$ @bobble It's Purely original, for a class I'm teaching! $\endgroup$
    – Outsider
    Mar 22 '21 at 23:55
  • $\begingroup$ Isn't the answer completely trivial? Or am I missing something? $\endgroup$
    – loopy walt
    Mar 23 '21 at 0:06
  • $\begingroup$ @loopywalt it is... lol $\endgroup$
    – Outsider
    Mar 23 '21 at 0:06

This seems pretty simple, but is the answer


This number in base 16 is

FEDEF, which is the largest five-digit palindrome in base 16 where each digit appears at most twice.


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