Really don't know, Pat. I've heard that 4 color thing, but in my graduate work I pretty well kept to the meat & potatoes of real & complex analysis and abstract algrebra. Only one course in topology and that was pretty straight math / set theory / logic. My undergraduate classes were a tad more varied (Boolean algrebra, number theory, differential equations, ring theory, some upper division probability and statistics courses that used calculus, etc) but never studied the 4 color thing as far as I can remember. Robert -----Original Message----- From: [log in to unmask] [SMTP:[log in to unmask]] Sent: Monday, March 12, 2001 3:36 PM To: [log in to unmask] Subject: Re: (VERY) OFF TOPIC - Map coloring In a message dated 3/12/01 5:16:17 PM Eastern Standard Time, [log in to unmask] writes: I meant "both rational and irrational numbers". Had problems with that insert / delete mode on the keyboard. Robert How did they arrive at 1200 for the number of possible arrangements? I think the number has to be much lower, at least for the way I was doing it, which is to assume that any map, no matter how large, can be broken down into modules of four shapes, each of which is colored in the 4 colors. There could be one, two, or three "leftover" shapes, but they can be treated as an incomplete module. The hard part is figuring how to construct any map from the 24 sets of color arrangments possible for any individual module. I think one might have to go back and make an accommodation for whether an individual module has 1, 2, or3 internal vertices that don't touch the perimeter of the module. But how did they compute the 1200? pat