document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=364935>Question 364935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (1 pt) (a) Among 47 people at least how many were born in the same month?\r<BR>\n" );
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document.write( "(b) Assuming that no one is born on Feb. 29 (leap day), how many people should be selected to guarantee that at least 6 were born on the same day, not considering the year?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #260165 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=260165\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have 47 people.\r<BR>\n" );
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document.write( "you want to know at least how many were born in the same month.\r<BR>\n" );
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document.write( "i would think that at least 4 people had to be born in the same month.\r<BR>\n" );
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document.write( "here's why.\r<BR>\n" );
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document.write( "12 months in a year.\r<BR>\n" );
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document.write( "if every 12 people were born in a different month, then out of 47 people, at least 4 people were born in the same month.\r<BR>\n" );
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document.write( "the arrangement of all 47 people would look like this:\r<BR>\n" );
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document.write( "first 12 people          1  2  3  4  5  6  7  8  9  10  11  12\r\n" );
document.write( "second 12 people         1  2  3  4  5  6  7  8  9  10  11  12\r\n" );
document.write( "third 12 people          1  2  3  4  5  6  7  8  9  10  11  12\r\n" );
document.write( "remaining 11 people      1  2  3  4  5  6  7  8  9  10  11    \r\n" );
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document.write( "you could have a minimum of 3 people that were born in the same month, but that doesn't answer the question.\r<BR>\n" );
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document.write( "the question is at least how many people were born in the same month.\r<BR>\n" );
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document.write( "that would have to be 4 because there is at least one case where 4 people were born in the same month.\r<BR>\n" );
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document.write( "assume there were 37 people, than what is the least number of people that were born in the same month?\r<BR>\n" );
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document.write( "here's the complete set of 37 people.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "first 12 people          1  2  3  4  5  6  7  8  9  10  11  12\r\n" );
document.write( "second 12 people         1  2  3  4  5  6  7  8  9  10  11  12\r\n" );
document.write( "third 12 people          1  2  3  4  5  6  7  8  9  10  11  12\r\n" );
document.write( "remaining 11 people      1  \r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "it's a little easier to see here.   there are a lot of people where 3 were born in the same month, but there is at least 1 case where 4 people were born in the same month, so the least number of people that were born in the same month still has to be 4.\r<BR>\n" );
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document.write( "that's my thinking, anyway.\r<BR>\n" );
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document.write( "your second problem:\r<BR>\n" );
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document.write( "(b) Assuming that no one is born on Feb. 29 (leap day), how many people should be selected to guarantee that at least 6 were born on the same day, not considering the year?\r<BR>\n" );
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document.write( "there are 365 days in the year.\r<BR>\n" );
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document.write( "assuming everybody was born on a different day, then you could have 365 people where nobody was born on the same day.\r<BR>\n" );
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document.write( "the 366 person, however, would have to have been born on the same day as somebody else in the group.\r<BR>\n" );
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document.write( "therefore, the minimum number of people in the group would have to be 366 to guarantee that at least 2 people were born on the same day.\r<BR>\n" );
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document.write( "but you wanted to guarantee that at least 6 people were born on the same day.\r<BR>\n" );
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document.write( "assuming you had 5 * 365 people together, with every 5 of them being born on the same day.\r<BR>\n" );
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document.write( "you would have a total of 365 * 5 = 1825 people, with no more than 5 people being born on the same day.\r<BR>\n" );
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document.write( "add 1 more person and you will be guaranteed that at least 6 people were born on the same day.\r<BR>\n" );
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document.write( "that comes out to be 1826 people.\r<BR>\n" );
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document.write( "1825 / 5 = 365 sets of people born on the same day, with each set containing no more than 5 people.\r<BR>\n" );
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document.write( "set 1 is the number of people born on day 1.<BR>\n" );
document.write( "set 2 is the number of people born on day 2.<BR>\n" );
document.write( "etc.\r<BR>\n" );
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document.write( "that next person had to be added to one of the sets of 5 to make it a set of 6.\r<BR>\n" );
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