document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204619>Question 1204619</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the set {1,2,3,5,8,13,21,34} which integers between 30 and 50 cannot be written as a number from the set on it’s own, or as the sum of either two or three numbers from the given set. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840976 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'm not sure why I included 4 in my previous answer, but here's a rewrite.\r<BR>\n" );
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document.write( "When considering 3 items from the set {1,2,3,5,8,13,21,34} we could have the following examples<BR>\n" );
document.write( "30 = 1+8+21<BR>\n" );
document.write( "31 = 2+8+21<BR>\n" );
document.write( "32 = 3+8+21<BR>\n" );
document.write( "<font color=red>NOT able to form 33</font><BR>\n" );
document.write( "34 = 5+8+21<BR>\n" );
document.write( "35 = 1+13+21<BR>\n" );
document.write( "36 = 2+13+21<BR>\n" );
document.write( "37 = 1+2+34<BR>\n" );
document.write( "38 = 1+3+34<BR>\n" );
document.write( "39 = 2+3+34<BR>\n" );
document.write( "40 = 1+5+34<BR>\n" );
document.write( "41 = 2+5+34<BR>\n" );
document.write( "42 = 3+5+34<BR>\n" );
document.write( "43 = 1+8+34<BR>\n" );
document.write( "44 = 2+8+34<BR>\n" );
document.write( "45 = 3+8+34<BR>\n" );
document.write( "<font color=red>NOT able to form 46</font><BR>\n" );
document.write( "47 = 5+8+34<BR>\n" );
document.write( "48 = 1+13+34<BR>\n" );
document.write( "49 = 2+13+34<BR>\n" );
document.write( "50 = 3+13+34<BR>\n" );
document.write( "possible sums = 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50\r<BR>\n" );
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document.write( "sums not able to be formed = <font color=red>33, 46</font>\r<BR>\n" );
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document.write( "Or if we consider 2 items from the set {1,2,3,5,8,13,21,34}, then,\r<BR>\n" );
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document.write( "34 = 13+21<BR>\n" );
document.write( "35 = 1+34<BR>\n" );
document.write( "36 = 2+34<BR>\n" );
document.write( "37 = 3+34<BR>\n" );
document.write( "39 = 34+5<BR>\n" );
document.write( "42 = 34+8<BR>\n" );
document.write( "47 = 13+34<BR>\n" );
document.write( "possible sums = 34, 35, 36, 37, 39, 42, and 47\r<BR>\n" );
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document.write( "sums we cannot form = 30, 31, 32, 33, 38, 40, 41, 43, 44, 45, 46, 48, 49, and 50\r<BR>\n" );
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document.write( "Answer: The only sums we cannot reach are <font color=red>33 and 46</font> when we're able to add 2 or 3 items from the set {1,2,3,5,8,13,21,34}<BR>\n" );
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