Solution: A matter of time

This is the solution to the Divertimento A matter of time.

Divertimento

There are people who don’t like to tell their age. One of them just says that if birthdays were only celebrated, as they should be, when the day of the year and the day of the week on which one was born coincide, this summer 2016 would have been his 9th birthday. How old is that person?

Solution

Let’s assume that the day of birth is a Monday. As 2016 is a leap year and summer goes after 29 February, this day in 2015 will be a Saturday. The previous years respectively will be

2015	Saturday
2014	Friday
2013	Thursday
2012	Wednesday
2011	Monday
2010	Sunday
2009	Saturday
2008	Friday
2007	Wednesday
2006	Tuesday
2005	Monday
2004	Sunday
2003	Friday
2002	Thursday
2001	Wednesday
2000	Tuesday
1999	Sunday
1998	Saturday
1997	Friday
1996	Thursday
1995	Tuesday
1994	Monday
1993	Sunday
1992	Saturday
1991	Thursday
1990	Wednesday
1989	Tuesday
1988	Monday

The birthday is again a Monday in a leap year and the cycle repeats itself. Thus, in this period of 5+6+11+6+6=28 years, there are 4 birthdays. The next cycle would take us to 1960. The next birthday takes us to 1955, which is the year of birth of the person, who has reached the age of 61.