athematics will have limited
utility in analyzing dates on the Gregorian
Calendar. Irregular durations for the months may
not be the only impediment to generalized algorithms.
There
is also the matter of leap
year, with its extra day added quadrennially.
No
intervals are divisible by seven except the duration of
February -- hey, in non-leap years. Accordingly,
the days of the week precess
drunkenly through the months.
If
we treat four consecutive years as a unit (quad-year,
let's call it), then one quad-year comprises 4 x 365 +
1 = 1,461 days, which is not divisible by seven.
By putting seven quad-years end-to-end, the resulting
10,227 days is divisible by seven and covers all
possible calendars. Seven consecutive quad-years
will repeat themselves exactly every 28 years.
As a finite domain, the puzzle can be
solved by determinism.
Your
spreadsheet is a handy tool for carrying out an
otherwise tedious process, and here are the results --
28 Magnanimous Months,
alongside the number of months in between...
July, 2011
March,
2013
August,
2014
May,
2015
January,
2016
July,
2016
December,
2017
March,
2019
May,
2020
January,
2021
October,
2021
July,
2022
December,
2023
March,
2024
August,
2025
May,
2026
January,
2027
October,
2027
December,
2028
March,
2030
August,
2031
October,
2032
July,
2033
December,
2034
August,
2036
May,
2037
January,
2038
October,
2038
|
19
16
8
7
5
16
14
13
7
8
8
16
2
16
8
7
8
13
14
16
13
8
16
19
8
7
8
8
|
This
pattern will repeat itself ad infinitum.
By inspection, then, here is the solution to the puzzle...
The times
between successive Magnanimous
Months range
between 2 months and 19
months.
|
Epilog
Twelve
years went by after the publication of Magnanimous Month.
Your puzzle-master received the following message:
This coming February cannot come in your
life again.
This year's February has...
4 Sundays
4 Mondays
4 Tuesdays
4 Wednesdays
4 Thursdays
4 Fridays
4 Saturdays
This happens once ever 823 years.
This is called miraclein.
The message goes on to promise miracles for immediate
forwardings to others.
Solvers recognize at once that every
February has exactly the same four-of- each
weekday distribution except in leap-years.
Indeed, every month of every year has at least
those same quantities plus bonuses of 0, 1, 2, or 3
days-of-the-week.
By the way, the word 'miraclein' cannot be
found in 55
dictionaries.
|