document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28343>Question 28343</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let's do a Koningsberg bridge problem for the city of New York.  We will ignore any tunnels and Staten Island since there is only one bridge to it which immediately makes it impossible.  Within the city I count the following:\r<BR>\n" );
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document.write( "11 bridges between Manhattan and the Bronx<BR>\n" );
document.write( "6 bridges between Manhattan and Queens/Brooklyn<BR>\n" );
document.write( "4 bridges between the Bronx and Queens/Brooklyn\r<BR>\n" );
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document.write( "Is it possible to make a tour of the city crossing every bridge only once and still return to the same starting point? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15410 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=15410\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Count the degree for each vertex:<BR>\n" );
document.write( " Manhattan:  11 + 6 = 17<BR>\n" );
document.write( " Bronx: 11 + 4 = 15<BR>\n" );
document.write( " Queens/Brooklyn: 6+4 =10\r<BR>\n" );
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document.write( " Note that there are two odd vertices, so the only possible Euler<BR>\n" );
document.write( "path is starting from Manhattan to Bronx (or reverse).\r<BR>\n" );
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document.write( " But, there is no Euler circuit which can return to the same starting point<BR>\n" );
document.write( " (unless all vertices are of even degree. why ?)\r<BR>\n" );
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document.write( " Kenny </SPAN>\n" );
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