TITLE: Simple problems that can be carried around in your head
QUESTION [7 upvotes]: What are some problems that can easily be carried around in your head and require no need of ink and paper? Problems like irrationality of $\sqrt2$  or infinitude of primes or Gauss's first initiation with number theory. 
I had and lost Mathematical Snippets. So I was hoping for something similar reference. Simple problems that I can take to shower, or during rush hour traffic, or for a walk, or waiting in a line in grocery or during a math lecture to entertain me. /nodisrespecttoprof. :]
Thank you so  much in advance!
EDIT: I am sorry, I actually had Math-A-Day in mind. But being a fan of Theoni Pappas I also bought the other one I mentioned.

REPLY [2 votes]: Look at Lewis Carroll's "Pillow Problems and a Tangled Tale"
(available on Amazon - published by Dover). 
These are problems he thought of to distract his mind from other things
and were intended to be worked on while lying in bed.
The problems concern themselves mainly with
geometry, algebra, and probability.