<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; "><DIV><DIV>Brendan McKay:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Monaco" size="5" style="font: 16.0px Monaco">A Jewish calendar on the web that has been thoroughly tested is here:</FONT></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Monaco" size="5" style="font: 16.0px Monaco"><SPAN class="Apple-converted-space"> </SPAN><A href="http://www.jewishgen.org/jos/">http://www.jewishgen.org/jos/</A></FONT></P></BLOCKQUOTE><BR></DIV><DIV>That's great. Thank you so much. I was able to tabulate the data available there and confirm that my formula agrees with it for the years 1753-2238. And using those dates, I can now revisit the original "Years when Ramadan and Rosh Hashana coincide" table:</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Year Ramadan <FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">Rosh Hashana</SPAN></FONT><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; "><BR style=""></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; ">1777 10/3 10/2</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; ">1778 9/23 9/22</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; ">1779 9/12 9/11</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; ">1810 9/30 9/29</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; ">1811 = 9/19 9/19</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; ">1812 9/8 9/7</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; ">1843 = 9/25 9/25</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; ">1844 = 9/14 9/14</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; ">1875 10/1 9/30</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; ">1876 9/20 9/19</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; ">1877 9/9 9/8</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 17.3px/normal Monaco; min-height: 22px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">1908 9/27 9/26</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">1909 = 9/16 9/16</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;"><BR class="khtml-block-placeholder"></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">1940 = 10/3 10/3*</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">1941 = 9/22 9/22*</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">1942 = 9/12 9/12</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;"><BR class="khtml-block-placeholder"></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">1973 9/28 9/27</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">1974 9/18 9/17*</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">1975 9/7 9/6</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;"><BR class="khtml-block-placeholder"></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2005 = 10/4 10/4</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2006 9/24 9/23</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2007 = 9/13 9/13</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;"><BR class="khtml-block-placeholder"></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2038 = 9/30 9/30*</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2039 = 9/19 9/19*</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2040 = 9/8 9/8</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;"><BR class="khtml-block-placeholder"></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2071 9/25 9/24</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2072 9/14 9/13*</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;"><BR class="khtml-block-placeholder"></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2103 10/3 10/2</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2104 9/21 9/20</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2105 = 9/10 9/10</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;"><BR class="khtml-block-placeholder"></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2136 = 9/27 9/27</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2137 = 9/16 9/16</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;"><BR class="khtml-block-placeholder"></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2168 = 10/3 10/3</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2169 9/22 9/21</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2170 9/12 9/11</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;"><BR class="khtml-block-placeholder"></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2201 9/30 9/29</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2202 9/19 9/18</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2203 = 9/8 9/8</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;"><BR class="khtml-block-placeholder"></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2233 10/6 10/5</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2234 = 9/25 9/25</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="5"><SPAN class="Apple-style-span" style="font-size: 17.3px;">2235 = 9/14 9/14</SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">*'s are corrected Rosh Hashana dates. Three consecutive coincidental years are rather special, appearing only twice: 1940-1942 and 2038-2040.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV></DIV></BODY></HTML>