document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=977381>Question 977381</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there tutors, I have no idea how to solve this, can u guys help me? Thanks\r<BR>\n" );
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document.write( "A hockey game between two teams is 'relatively close' if the number of goals scored by the two teams never differ by more than two. In how many ways can the first 12 goals of a game be scored if the game is 'relatively close'? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #598965 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=598965\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You're going to need a large sheet of paper and draw out all of the possible outcomes.<BR>\n" );
document.write( "Let's call the two teams A and B. <BR>\n" );
document.write( "Let's start by looking at the first goal, either A or B scores.<BR>\n" );
document.write( "Then the second, again either A or B.<BR>\n" );
document.write( "So the four possible outcomes are,<BR>\n" );
document.write( "AA<BR>\n" );
document.write( "AB<BR>\n" );
document.write( "BA<BR>\n" );
document.write( "BB<BR>\n" );
document.write( "TO get the next set, just add an A and then a B to each previous outcome so for each previous outcomes, you'll get two new outcomes.<BR>\n" );
document.write( "Now the third goal, no team can score three in a row or more so the possible outcomes are,<BR>\n" );
document.write( "AAA <--- Not allowed<BR>\n" );
document.write( "AAB <BR>\n" );
document.write( "ABA<BR>\n" );
document.write( "ABB<BR>\n" );
document.write( "BAA<BR>\n" );
document.write( "BAB<BR>\n" );
document.write( "BBA<BR>\n" );
document.write( "BBB <--- Not allowed<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Fourth goal<BR>\n" );
document.write( "AABA<BR>\n" );
document.write( "AABB<BR>\n" );
document.write( "ABAA<BR>\n" );
document.write( "ABAB<BR>\n" );
document.write( "ABBA<BR>\n" );
document.write( "ABBB <--- Not allowed<BR>\n" );
document.write( "BAAA <--- Not allowed<BR>\n" );
document.write( "BAAB<BR>\n" );
document.write( "BABA<BR>\n" );
document.write( "BABB<BR>\n" );
document.write( "BBAA<BR>\n" );
document.write( "BBAB<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Fifth goal<BR>\n" );
document.write( "AABAA<BR>\n" );
document.write( "AABAB<BR>\n" );
document.write( "AABBA<BR>\n" );
document.write( "AABBB <--- Not allowed<BR>\n" );
document.write( "ABAAA <--- Not allowed<BR>\n" );
document.write( "ABAAB<BR>\n" );
document.write( "ABABA<BR>\n" );
document.write( "ABABB<BR>\n" );
document.write( "ABBAA<BR>\n" );
document.write( "ABBAB<BR>\n" );
document.write( "BAABA<BR>\n" );
document.write( "BAABB<BR>\n" );
document.write( "BABAA<BR>\n" );
document.write( "BABAB<BR>\n" );
document.write( "BABBA<BR>\n" );
document.write( "BABBB <--- Not allowed<BR>\n" );
document.write( "BBAAA <--- Not allowed<BR>\n" );
document.write( "BBAAB<BR>\n" );
document.write( "BBABA<BR>\n" );
document.write( "BBABB<BR>\n" );
document.write( "And so on until you get to 12 goals.<BR>\n" );
document.write( "It's not difficult but it is tedious and you can easily make a mistake. <BR>\n" );
document.write( "Just make sure you have twice the number of outcomes of the previous series before you start knocking out \"Not allowed\" goals to keep tabs on your work. <BR>\n" );
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document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can also generate all 2^12 (4096) possible outcomes and then go through and knockout the ones that have more than 2 in a row for either team. Six and 1/2 dozen the other.<BR>\n" );
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