document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=629158>Question 629158</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Imagine that you have a set of integers e.g. {1, 2, 3, 4, 5, 6}.<BR>\n" );
document.write( "In how many ways can we form groups of size 1,2,...6, by taking into account that we only can group consecative numbers (and of course single).\r<BR>\n" );
document.write( "\n" );
document.write( "For example, some examples are:<BR>\n" );
document.write( "1)    {1} {2} {3} {4} {5} {6} (6 groups)<BR>\n" );
document.write( "2)    {1,2} {3,4} {5,6} (3 groups)<BR>\n" );
document.write( "3)    {1} {2,3} {4,5} {6} (4 groups)<BR>\n" );
document.write( "4)    {1,2,3,4,5,6} (1 group)<BR>\n" );
document.write( "and so on.....  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #396061 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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/cgi-bin/show-face.mpl?user=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=396061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Think of this string:\r<BR>\n" );
document.write( "\n" );
document.write( "      A1B2C3D4E5F6G\r<BR>\n" );
document.write( "\n" );
document.write( "We must choose a left bracket \"{\" to go where the A is.  That's 1 way.\r<BR>\n" );
document.write( "\n" );
document.write( "We may either choose \"} {\" or a comma \",\" to go where the B is.  That's 2 ways.\r<BR>\n" );
document.write( "\n" );
document.write( "We may either choose \"} {\" or a comma \",\" to go where the C is.  That's 2 ways.\r<BR>\n" );
document.write( "\n" );
document.write( "We may either choose \"} {\" or a comma \",\" to go where the D is.  That's 2 ways.\r<BR>\n" );
document.write( "\n" );
document.write( "We may either choose \"} {\" or a comma \",\" to go where the E is.  That's 2 ways.\r<BR>\n" );
document.write( "\n" );
document.write( "We may either choose \"} {\" or a comma \",\" to go where the F is.  That's 2 ways.\r<BR>\n" );
document.write( "\n" );
document.write( "We must choose a right bracket \"}\" to go where the G is.  That's 1 way.\r<BR>\n" );
document.write( "\n" );
document.write( "Answer: 1󫎾󫎾󫎽 = 32 ways.\r<BR>\n" );
document.write( "\n" );
document.write( "Edwin</pre>\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );