document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=696395>Question 696395</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Every year there is at least one Friday the thirteenth, but no year has more than 3. On 1998 there are exactly 3: in Feb, Mar, Nov. When will the next year be that contains exactly 3 friday the thirteen's? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #429065 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=429065\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A leap year (like 2000, 2004, and 2008) has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=366=7%2A52%2B2 ALIGN=MIDDLE  ALT=\"366=7%2A52%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > days,<BR>\n" );
document.write( "52 weeks plus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > extra weekdays.<BR>\n" );
document.write( "All other years (including 1998) have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=365=7%2A52%2B1 ALIGN=MIDDLE  ALT=\"365=7%2A52%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > days,<BR>\n" );
document.write( "52 weeks plus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > extra weekday.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Each extra weekday causes the days of the week to shift by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > day.<BR>\n" );
document.write( "If the thirteenth of a month was a Friday,<BR>\n" );
document.write( "a year later the same date will be a Saturday if no leap day is involved,<BR>\n" );
document.write( "but it will be a Sunday if there was a February 29 in between.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The only way to have 3 Friday the thirteenths on a year that is not a leap year is to have the pattern of 1998,<BR>\n" );
document.write( "with Feb-13, Mar-13 and Nov-13 being Fridays.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The pattern from 1998 will repeat if there is a shift of a whole number of weeks (7 days, or a multiple of 7 days).<BR>\n" );
document.write( " <BR>\n" );
document.write( "Five years after Feb-13-1998, it will be Feb-13-2003, and having had Feb-29-2000 in between the weekdays will have shifted by 6 days, so it will be Thursday.<BR>\n" );
document.write( "A year later, Feb-13-2004 will be Friday,<BR>\n" );
document.write( "but with Feb-29-2004 coming up, the 1998 pattern will not repeat.<BR>\n" );
document.write( "Leap years have 3 Friday the thirteenths only if January 13 is a Friday.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Four years after Feb-13-2004, it will be Feb-13-2008.<BR>\n" );
document.write( "With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > years and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > leap day in between (Feb-29-2004 and Feb-29-2008),<BR>\n" );
document.write( "the weekdays will have shifted <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B1=5 ALIGN=MIDDLE  ALT=\"4%2B1=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > days, and it will be Wednesday.<BR>\n" );
document.write( "January 13, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31=7%2A4%2B3 ALIGN=MIDDLE  ALT=\"31=7%2A4%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > days earlier, will have been a Sunday, and 2008 will not have 3 Friday the thirteenths.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Five years after Feb-13-2004, it will be Feb-13-2009.<BR>\n" );
document.write( "With two <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > years and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > leap days in between (Feb-29-2004 and Feb-29-2008),<BR>\n" );
document.write( "the weekdays will have shifted <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2B2=7 ALIGN=MIDDLE  ALT=\"5%2B2=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > days, and it will be Friday again.<BR>\n" );
document.write( "And because 2009 is not a leap year, the pattern of 1998 will repeat.<BR>\n" );
document.write( "After 1998, the next year that contains exactly 3 Friday the thirteens is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282009%29 ALIGN=MIDDLE  ALT=\"highlight%282009%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );