document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1080516>Question 1080516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, how would I work this question out? Thank for your help in advance:)<BR>\n" );
document.write( "A partition of an integer into distinct positive parts (no two are equal) is called an unequal partition. For example, there are seven unequal partitions of 12 into 3 parts: 12= 9+2+1 = 8+3+1 = 7+4+1 = 7+3+2 = 6+5+1 = 6+4+2 = 5+4+3. <BR>\n" );
document.write( "The span of a partition is the difference between the smallest and largest number in the partition. For example, the spans of the unequal partitions of 12 into 3 parts listed above are respectively 8,7,6,5,5,4,2. Thus 2 is the smallest span of an unequal partition of 12 into 3 parts. \r<BR>\n" );
document.write( "\n" );
document.write( "a. Find at least two unequal partitions of 2017 into 5 parts with a span of 7.\r<BR>\n" );
document.write( "\n" );
document.write( "b. Find an unequal partition of 2017 into 5 parts with the smallest possible span.\r<BR>\n" );
document.write( "\n" );
document.write( "c. Find the smallest number that has an unequal partition into 5 parts. Describe the set of all numbers that have an unequal partition into 5 parts with a span of 4.\r<BR>\n" );
document.write( "\n" );
document.write( "d. Show that for each number that has an unequal partition into 5 parts, the smallest span for such partitions is 4 or 5. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #694681 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=694681\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll at least get you started.<BR>\n" );
document.write( "Such a large number with a small span means the numbers are close to each other.<BR>\n" );
document.write( "Dividing 2017 by 5 gives you 404.5. <BR>\n" );
document.write( "So start with numbers around there.<BR>\n" );
document.write( "I used EXCEL typing numbers into 4 cells and calculating the last one (since the sum equals 2017). <BR>\n" );
document.write( "Then changed numbers around.<BR>\n" );
document.write( "(401,402,403,404,407) gives you 6.<BR>\n" );
document.write( "(401,402,403,405,406) gives you 5.<BR>\n" );
document.write( "(399,403,404,405,406) gives you 7.<BR>\n" );
document.write( "a) Play around to get another. <BR>\n" );
document.write( "b) I think its 5 but play around to see if you can find one lower.<BR>\n" );
document.write( "c) It should be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B2%2B3%2B4%2B5=15 ALIGN=MIDDLE  ALT=\"1%2B2%2B3%2B4%2B5=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > with a span of 4.<BR>\n" );
document.write( "All numbers would then increment by 1,<BR>\n" );
document.write( "So the sums would increase by 5(1) or 5.<BR>\n" );
document.write( "15,20,25,30,35,40,.... with a span of 4.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );