A simple decision problem whose decidability is not known I am preparing for a talk aimed at undergraduate math majors, and as part of it, I am considering discussing the concept of decidability.  I want to give an example of a problem that we do not currently know to be decidable or undecidable.  There are many such problems, but none seem to stand out as nice examples so far.

What is a simple-to-describe decision problem whose decidability is open?
The Matrix Mortality Problem for 2x2 matrices.  I.e., given a finite list of 2x2 integer matrices M1,...,Mk, can the Mi's be multiplied in any order (with arbitrarily many repetitions) to produce the all-0 matrix?

(The 3x3 case is known to be undecidable.  The 1x1 case, of course, is decidable.)