The #PuzzleForToday is rubbish, for a variety of reasons. Yesterday's was particularly egregious - more a "guess what I'm thinking" riddle.
What would a positive version of the segment look like?
My starting point: 30 seconds of maths that you can think about for up to 10 minutes

Puzzles are fun, but unless you do lots of them, the vast majority of the time you'll bounce straight off them.
It's too easy, as seen in the Puzzle for Today, to dress up a fun maths fact as a puzzle, when just saying the fact would be just as satisfying.

However, puzzles give you a way of taking a family of problems that is completely understood in the abstract, and picking particular instances that still take some brainpower to solve. For example, I can write a general algorithm to solve sudokus, but I still enjoy them