Problem suggestions for polymath for undergraduates research I'm inspired by the polymath project. It might be great for few undergraduates to work together on a research topic.
What are some research problems with the following properties(Experimental mathematics is a field containing problems with the criteria below):


*

*Accessible to undergraduates

*There can be many reasonable approaches to the problem

*People with computer science, applied math or other related backgrounds can also contribute

 A: I don't know about the polymath project but here is one thought:
A long knot is an embedding of $\mathbb{R}\rightarrow\mathbb{R}^3$ which as $t$ tends to $\pm\infty$ approach the line $x=y=z$. Examples are given by $t\mapsto (x(t),y(t)z(t))$
where $x(t)$, $y(t)$, $z(t)$ are monic polynomials of degree $2r+1$. In fact all long knots arise this way. However when I have implemented this you get pretty unsatisfactory pictures. The problem is to find a way to get better pictures (not exactly cutting edge research, I know).
One possibility would be to define an energy functional and then take the gradient flow to find a local minimum. If we fix $r$ this all takes place on a finite dimensional manifold.
Another direction is to apply a Mobius transformation that moves the point at infinity. This gives a knot parametrised by rational functions. I haven't tried this, but I doubt it gives a pretty picture. Can these pictures be improved?
You could also investigate this from the point of view of Vassiliev theory (which is how it came up when I heard about it). That is, look at the discriminant, the polynomials whose long knots have self-intersections.
A: Pick any of the problems in the archives of Al Zimmermann's Programming Contests, and make progress either on the theoretic side (tighter upper bounds / lower bounds / asymptotics) or the computational side.
A specific nice example could be Point Packing. 
A: Consider this generalization of the $N$-queens problem:

The $N + k$ Queens Problem: Let $N > 0$ and $k \geq 0$ be integers. On an $N \times N$
  chessboard, can you place $N + k$ queens and $k$ pawns so that any two queens on the
  same row, column, or diagonal have at least one pawn between them?

We've had many math and computer science undergraduates working on projects related to this problem.  For more information, please see the $N + k$ Queens Problem Page at http://npluskqueens.info .
A: I hope the question about sign matrices here maybe of interest to some undergraduates like me. It certainly also offers a programming experience. Let me know if any get interested. I will be happy to correspond. 
