|
In this time period, 27759 days of birth were considered, of which 3648 were days in which the nth golden birthday would be triggered. The fraction is 64/487, or about 0.131416837782341.
It turns out that only 7 dates of the month make this possible. They are listed below with the number of occurrences of each within the 76-year period.
date 5 6 11 17 22 23 28
occurrences 228 456 684 684 456 228 912
The 912 for the 28th of the month stands out, as 12*76. It results from the fact that within this time span the cycle of year types is 28 years long, repeating the yearly calendar (though irregular such repeats occur within the cycle), so everyone's 28th birthday occurs on the same day of the week as his day of birth. Only years like 1900 or 2100 disrupt this cycle.
y=1950; m=1; d=1; dList=[]; idList=[];
ct=0; yList=[]; considered=0;
dayCt=zeros(1,31);
dt=datetime(y,m,d);
while y<2026
dt2=datetime(y+d,m,d);
considered=considered+1;
if month(dt2)==m % leap->non-leap gives March vs Feb
if weekday(dt)==weekday(dt2)
ct=ct+1;
dayCt(day(dt))=dayCt(day(dt))+1;
% if ~ismember(year(dt),yList)
% yList(end+1)=year(dt);
% end
if ~ismember(day(dt),dList)
dList(end+1)=day(dt);
end
did=100*month(dt)+day(dt);
if ~ismember(did,idList)
idList(end+1)=did;
end
end
end
jd=juliandate(dt)+1;
dt=datetime(jd,'ConvertFrom','juliandate');
y=year(dt);
m=month(dt);
d=day(dt);
end
ct
considered
sym(ct/considered)
ct/considered
dayCt=dayCt(dList);
[dList,idx]=sort(dList);
dList
dayCt(idx)
ct =
3648
considered =
27759
ans =
64/487
ans =
0.131416837782341
dList =
5 6 11 17 22 23 28
ans =
228 456 684 684 456 228 912
|
