a set of diophantine equations relating father and son...

bday.rb

# Interesting relationships:

# Say the father's age is 72 and the son's age is 40.
# The father was born in 1940 and the son in 1972.

# Isn't that curious?

# In english, the dad's age is the current year minus the dad's birth year,
# the right-most 2 digits of the dad's birth year is the son's age,
# the son's age is the current year minus the son's birth year,
# and the right-most 2 digits of the son's birth year is the dad's age,
# and the son was born at least 12 years after the dad.

# Or in math form, the system of diophantine equations:

# D=T-D_0 \\
# D_0 \pmod{100} = S \\
# S = T-S_0 \\
# S_0 \pmod{100} = D \\
# S_0 > D_0 + 12


time_range = (1900..2100)
son_years = time_range
dad_years = time_range
#time_range = (2012..2012)

time_range.each do |t|
  dad_years.each do |dad_dob|
    son_years.each do |son_dob|
      next if son_dob < (dad_dob + 12)
      dad_age = t - dad_dob
      son_age = t - son_dob
      if dad_dob.modulo(100) == son_age && son_dob.modulo(100) == dad_age
        #puts "t=#{t};  dad_dob: #{dad_dob} (#{dad_age}), son_dob: #{son_dob} (#{son_age})"
        puts "#{t},#{dad_dob},#{son_dob}"
      end
    end
  end
end

# prints the possible solutions of this system over time, e.g. for this year:
# t=2012;  dad_dob: 1913 (99), son_dob: 1999 (13)
# t=2012;  dad_dob: 1914 (98), son_dob: 1998 (14)
# t=2012;  dad_dob: 1915 (97), son_dob: 1997 (15)
# t=2012;  dad_dob: 1916 (96), son_dob: 1996 (16)
# t=2012;  dad_dob: 1917 (95), son_dob: 1995 (17)
# t=2012;  dad_dob: 1918 (94), son_dob: 1994 (18)
# t=2012;  dad_dob: 1919 (93), son_dob: 1993 (19)
# t=2012;  dad_dob: 1920 (92), son_dob: 1992 (20)
# t=2012;  dad_dob: 1921 (91), son_dob: 1991 (21)
# t=2012;  dad_dob: 1922 (90), son_dob: 1990 (22)
# t=2012;  dad_dob: 1923 (89), son_dob: 1989 (23)
# t=2012;  dad_dob: 1924 (88), son_dob: 1988 (24)
# t=2012;  dad_dob: 1925 (87), son_dob: 1987 (25)
# t=2012;  dad_dob: 1926 (86), son_dob: 1986 (26)
# t=2012;  dad_dob: 1927 (85), son_dob: 1985 (27)
# t=2012;  dad_dob: 1928 (84), son_dob: 1984 (28)
# t=2012;  dad_dob: 1929 (83), son_dob: 1983 (29)
# t=2012;  dad_dob: 1930 (82), son_dob: 1982 (30)
# t=2012;  dad_dob: 1931 (81), son_dob: 1981 (31)
# t=2012;  dad_dob: 1932 (80), son_dob: 1980 (32)
# t=2012;  dad_dob: 1933 (79), son_dob: 1979 (33)
# t=2012;  dad_dob: 1934 (78), son_dob: 1978 (34)
# t=2012;  dad_dob: 1935 (77), son_dob: 1977 (35)
# t=2012;  dad_dob: 1936 (76), son_dob: 1976 (36)
# t=2012;  dad_dob: 1937 (75), son_dob: 1975 (37)
# t=2012;  dad_dob: 1938 (74), son_dob: 1974 (38)
# t=2012;  dad_dob: 1939 (73), son_dob: 1973 (39)
# t=2012;  dad_dob: 1940 (72), son_dob: 1972 (40)
# t=2012;  dad_dob: 1941 (71), son_dob: 1971 (41)
# t=2012;  dad_dob: 1942 (70), son_dob: 1970 (42)
# t=2012;  dad_dob: 1943 (69), son_dob: 1969 (43)
# t=2012;  dad_dob: 1944 (68), son_dob: 1968 (44)
# t=2012;  dad_dob: 1945 (67), son_dob: 1967 (45)
# t=2012;  dad_dob: 1946 (66), son_dob: 1966 (46)
# t=2012;  dad_dob: 1947 (65), son_dob: 1965 (47)
# t=2012;  dad_dob: 1948 (64), son_dob: 1964 (48)
# t=2012;  dad_dob: 1949 (63), son_dob: 1963 (49)
# t=2012;  dad_dob: 1950 (62), son_dob: 1962 (50)
# t=2012;  dad_dob: 2000 (12), son_dob: 2012 (0)

Graphical results are here: Results