document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209105>Question 1209105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My street hockey team plays three games each week.  My team lost all $9$ games in the first three weeks. Then, my team won one game and lost two games in the fourth week, bringing our record to $1$ win and $11$ losses. Each week after that, my team won one game and lost two games.  My team first wins at least $60\%$ of all its games by the end of the first $n$ weeks.  What is $n$? </SPAN>\n" );
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document.write( "first three weeks: won 0 games out of 9 games total<BR>\n" );
document.write( "through 4 weeks: won 1 game out of 12 games total<BR>\n" );
document.write( "through 5 weeks: won 2 games out of 15 games total<BR>\n" );
document.write( "through 6 weeks: won 3 games out of 18 games total<BR>\n" );
document.write( "...etc...<BR>\n" );
document.write( "through n weeks: won n-3 games out of 3n games total\r<BR>\n" );
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document.write( "Divide the win count over the total, and multiply by 100, to get the win percentage<BR>\n" );
document.write( "For instance if you won A = 3 games out of B = 18 total then winPercentage = (100%)*A/B = (100%)*3/18 = 16.67% approximately\r<BR>\n" );
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document.write( "This means 100*(n-3)/(3n) represents the win percentage through the n<sup>th</sup> week.\r<BR>\n" );
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document.write( "As n gets bigger and bigger, the win percentage will slowly approach 100*n/(3n) = 100*(1/3) = 33.3% approximately. It will never reach this value since this is an asymptote. <BR>\n" );
document.write( "So the upper bound is that you'll win a third of your games if you play out to infinity and this pattern of \"1 win, 2 losses\" continues.<BR>\n" );
document.write( "This should be fairly obvious because for any given week you win 1 game out of 3 total. <BR>\n" );
document.write( "It's <u><font color=red>not</font></u> possible to win 60% of your games no matter how large n gets.<BR>\n" );
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