--part1_dd.116bb2ba.27deb75e_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit 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 --part1_dd.116bb2ba.27deb75e_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit <HTML><FONT FACE=arial,helvetica><FONT SIZE=3 FAMILY="SANSSERIF" FACE="Arial Narrow" LANG="0"><B>In a message dated 3/12/01 5:16:17 PM Eastern Standard Time, <BR>[log in to unmask] writes: <BR> <BR></FONT><FONT COLOR="#000000" SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0"></B> <BR><BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">I meant "both rational and irrational numbers". Had problems with that <BR>insert / delete mode on the keyboard. <BR> <BR>Robert <BR> <BR> </FONT><FONT COLOR="#000000" SIZE=3 FAMILY="SANSSERIF" FACE="Arial" LANG="0"></BLOCKQUOTE> <BR></FONT><FONT COLOR="#000000" SIZE=3 FAMILY="SANSSERIF" FACE="Arial Narrow" LANG="0"><B> <BR>How did they arrive at 1200 for the number of possible arrangements? I think <BR>the number has to be much lower, at least for the way I was doing it, which <BR>is to assume that any map, no matter how large, can be broken down into <BR>modules of four shapes, each of which is colored in the 4 colors. There could <BR>be one, two, or three "leftover" shapes, but they can be treated as an <BR>incomplete module. The hard part is figuring how to construct any map from <BR>the 24 sets of color arrangments possible for any individual module. I think <BR>one might have to go back and make an accommodation for whether an individual <BR>module has 1, 2, or3 internal vertices that don't touch the perimeter of the <BR>module. <BR> <BR>But how did they compute the 1200? <BR> <BR>pat</B></FONT></HTML> --part1_dd.116bb2ba.27deb75e_boundary--