document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182758>Question 1182758</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sport of bingbong involves two players. Each match consists of a number of rounds and each round consists of a number of points. The first player to win four points in a round wins the round. The first player to win six rounds in a match wins the match.<BR>\n" );
document.write( "Suppose that after a match of bingbong, the winner has won W points while the loser has won L points. What is the largest possible value of L-W? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813020 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813020\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose there are two players A and B, and assume that A has won the game. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It is quite apparent that the maximum number of rounds the game could have taken was 11, with A winning 6 of those rounds and B winning the other five, with A <BR>\n" );
document.write( "winning the 11th and final round. To maximize the value of L-W, we determine the scenario where A has won by the slimmest of margins, i.e., 4 - 3 (in 6 games), and <BR>\n" );
document.write( "lost by the widest of margins, i.e., 0 - 4 (in 5 games).  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The largest value of L-W would then be 6*3 + 5*4 - (6*4 + 5*0) = 18 + 20 - 24 = 14. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );