2010 --- Friday
2011 --- Saturday
2013 --- Tuesday
2014 --- Wednesday
2015 --- Thursday
2017 --- Sunday
2018 --- Monday
Now we can represent any non-Leap year with the above 7 calendars. Looking at the leap year cycle, we see that each one begins 5 days (2 + 1 + 1 + 1) after the previous leap year. When we look at the multiples of 5, mod 7:
5 = 5 mod 7
10 = 3 mod 7
15 = 1 mod 7
20 = 6 mod 7
25 = 4 mod 7
30 = 2 mod 7
35 = 0 mod 7
We can see that any sequence of 7 consecutive leap years will give us a full set of starting days. So, to complete our full calendar set:
Year --- Starting Day --- Leap Day
======================
2012 --- Sunday --- Wednesday
2016 --- Friday --- Monday
2020 --- Wednesday --- Saturday
2024 --- Monday --- Thursday
2028 --- Saturday --- Tuesday
2032 --- Thursday --- Sunday
2036 --- Tuesday --- Friday
To build a complete set, we would need the 14 years:
2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2020, 2024, 2028, 2032, and 2036
solution
