document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044685>Question 1044685</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When the eggs in a basket are grouped into 2,3, or 5 , there is always one extra. What is the least number of eggs for this grouping to be done? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #660031 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=660031\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We can brute-force our way to a solution:\r<BR>\n" );
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document.write( "1 modulo 2 ===> 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29, 31<BR>\n" );
document.write( "1 modulo 3 ===> 1,4,7,10,13,16,19,22,25,28,31<BR>\n" );
document.write( "1 modulo 5 ===> 1,6,11,16,21,26,31\r<BR>\n" );
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document.write( "Barring the possibility that there is only one egg, the least number of eggs for this grouping to be done is 31.\r<BR>\n" );
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document.write( "(There is a conventional method of doing this problem, by means of the chinese remainder theorem, but the <BR>\n" );
document.write( "solution above should suffice.)<BR>\n" );
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