document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1188291>Question 1188291</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In how many ways can 25 be expressed as the sum of three prime numbers?<BR>\n" );
document.write( "A) 1  B) 3  C) 4  D) 5  E) 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819342 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=819342\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Do some work on this yourself to find the answer.<br><BR>\n" );
document.write( "There is only one even prime number, 2.<BR>\n" );
document.write( "The sum of any two odd prime numbers is even.<BR>\n" );
document.write( "The desired sum of three prime numbers is 25, which is odd.<br><BR>\n" );
document.write( "Therefore, the sum of 25 must be using three odd primes.<br><BR>\n" );
document.write( "Note that, the way the problem is written, it is allowable for two of the three odd prime numbers to be the same.<br><BR>\n" );
document.write( "So......<br><BR>\n" );
document.write( "(1) If the smallest of the three odd prime numbers is 3, then the sum of the other two must be 22.<BR>\n" );
document.write( "(2) If the smallest of the three odd prime numbers is 5, then the sum of the other two must be 20.<BR>\n" );
document.write( "(3) If the smallest of the three odd prime numbers is 7, then the sum of the other two must be 18.<br><BR>\n" );
document.write( "Clearly the smallest of the three odd prime numbers can't be 11 or more.<br><BR>\n" );
document.write( "So look for solutions in each of the three cases.  Only simple addition is required.<br><BR>\n" );
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