However, I should point out that in order to see the full pattern that emerges it is necessary to test for ~400 years. This makes sense of course, given the (Gregorian Calendar) Leap Year Rules.

The output from the following (modified from my original) code gives an indication of the pattern:

#!/usr/bin/perl -l
use strict;
use warnings;
use Date::Calc qw/Days_in_Month Day_of_Week/;

my @days_of_week = qw/Mon Tue Wed Thu Fri Sat Sun/;
my $cnt;
my @cnt;

for my $year (1 .. 2500) {

    my %days_of_month;

    for my $month_of_year(1 .. 12) {
        for my $day_of_month(1 .. Days_in_Month($year,$month_of_year))
+ {
            my $dow = Day_of_Week($year,$month_of_year,$day_of_month);
            $days_of_month{$day_of_month}{$days_of_week[--$dow]}++;
        }
    }

    for my $day_of_month (sort {$a <=> $b} keys %days_of_month) {
        next if scalar keys %{$days_of_month{$day_of_month}} == 7;
        my @missing_days;
        for (@days_of_week) {
            push (@missing_days, $_) if !defined $days_of_month{$day_o
+f_month}{$_};
        }
        $cnt++;
        if ($missing_days[0] eq 'Sun') {
            push @cnt, $cnt;
            if ($cnt == 11) {
                print "$year:@cnt";
                @cnt = ();
            }
            $cnt = 0;
        }
    }
}
[download]

However, it's not so much the pattern that I found interesting - but the fact that every year it's _always_ the same day of the month (31st) that doesn't occur on every day of the week.

Cheers,
Darren :)

It might be related to the fact that there are only seven 31s in a year compared to 11 for 29 and 30 and 12 for all lower numbers :-) (I originaly thought that it's because there are only 6 31s, but that was before I counted them.) In either case it's easier to miss one of seven days if you only have seven attempts than if you have 11 or 12.

Jenda


Support Denmark! Defend the free world!

#!/usr/bin/perl
use strict;
use warnings;
use Date::Calc qw/Days_in_Month Day_of_Week/;

my @days_of_week = qw/NULL Mon Tue Wed Thu Fri Sat Sun/;

my $i=0;
# Our 14 calendars are in these years, this century
# see: http://www.koshko.com/calendar/calendar-lookup-gregorian.shtml
for (6, 7, 1, 2, 3, 10, 11, 12, 24, 8, 20, 4, 16, 0) {
  my $year=$_+2000;
  $i++;

  my %days_of_month;

  for my $month_of_year(1 .. 12) {
    my $sday = Day_of_Week($year,$month_of_year,1); # only need to cal
+l this once
    for my $day_of_month(1 .. Days_in_Month($year,$month_of_year)) {
      $sday = 1 if($sday>7);
      my $dow = $sday++;
      $days_of_month{$day_of_month}{$dow}++;
    }   
  }

  for my $day_of_month (sort keys %days_of_month) {
    next if(scalar keys %{$days_of_month{$day_of_month}} == 7); 
    my @missing_days;
    for (1..7) {
      push (@missing_days, $days_of_week[$_]) if !defined $days_of_mon
+th{$day_of_month}{$_};
    }   
    print "Calendar $i: In $year, Day $day_of_month does not fall on "
+, join(", ", @missing_days), "\n";
  }
}
[download]