Pat Bellew poses this nice parabola permutation problem:
Here is an interesting excursion to try; take a quadratic equation that you know has rational roots, and then permute the values of A, B, and C through all possible variations. What is the probability that they would ALL have rational roots?
Read his post at: http://pballew.blogspot.com/2011/10/permuations-of-coefficents-in-quadratic.html
I even like the question: so that each permutation has roots!