If you don't mind it being a simple and unoriginal idea:
A program where "how many monkeys, indeed, does it take to eventually write out Hamlet... or maybe just the first page of it" is asserted.
Not by truely randomly doing 100 random threads of totally random characters until one gets it right... but some other way. Maybe ... giving the chances for a monkey to type the correct character a boost each time one monkey gets it.
Also, kill monkey after each mistake.
Maybe add the ability for text files to be read, or strings to be typed.
((Was an idea bouncing around a long time ago that I just fished out. I might do this sometime soon XD
Sadly, it's not original...Probably dozens of these programs sitting in unused and unloved sectors of old harddrives globally.))
A program in which there is a parabola, and you can shine light (represented by a line or multiple lines) so it reflects. Light disappears where it hits the focus of the parabola.
A program which hashes, or just sends through an algorithm, a string and turns it into random notes that would let you 'hear' the string.
Sound might be hard to do, I guess o_o
Viewpoint of a soccerball being kicked across the world in 3D glory.
a program in which when the user draws a polygon on the screen, the weight/area centre of it is found and displayed.
Might have to restrict to triangles and squares...
Are these the kinds of ideas you need? Or are they too simple, too hard, takes too long...?