I discovered this problem midway in my reading of the book The Cuckoo's Egg by Clifford Stoll. The problem is stated but its solution is not provided within the pages of the book. Hint: The biology of self-replication is self-referential, as embodied by DNA and RNA replication mechanisms. The mathematician John Horton Conway discusses this sequence in the following YouTube video. https://www.youtube.com/watch?v=ea7lJkEhytA
Once I solved the problem, I coded it in Texas Instruments TI-83+ BASIC using $trings (lists in Scratch). Since I've coded the problem once I'm not motivated to code it in Scratch so I leave that for you do do if you're interested.