Counter-Example for Computability I am a retired college teacher, now trying to teach computing to middle school kids.  One of the parts of the definition of "algorithm" is that it must be "effectively computable."  I'm looking for an example that is not Turing computable.  I've used "solve world hunger" in the past, but but that seems fuzzy and amorphous.

Today I've spent some time with "Label an arbitrary statement as true or false," but I can't make it sing in a way that kids will say, "Yeah... that's right."  Busy Beaver and the halting problem are both too complicated to explain in a few minutes.  (I know about Scooping the Loop Snooper and have even assigned it as reading, but it would still take too much classroom time.)

Suggestions, either of new ideas or of a way to make "Label an arbitrary statement..." sing to the students would be most appreciated.
Strachey's proof for the Halting Problem is accessible to anyone who accepts reasoning by contradiction.

See 
https://academic.oup.com/comjnl/article/7/4/313/354243