Many delegates at "conference" relish the opportunity, and the space, to "do some mathematics". Opportunity and space help to make the experience memorable, but how often is the quality of the starting point, or question acknowledged? Here is a set of starting points or problems that invite the reader to "do some mathematics". Deliberately, no solutions are prescribed, or offered by the author who extends an invitation to readers and/or their students to submit their own deliberations by email. But, if you choose to keep any solution to yourself then so be it, as with much of mathematics it is said to be just as important to travel as it is to arrive.