50 weeks = 350 days.
C − A = 350 days, A − B = 300 days
⇒ C − B = 650 days.
650 ÷ 7 = 92 weeks + remainder 6 days.
So, B’s birthday = 6 days before Tuesday = Wednesday.
Solution:
Day shifts year-to-year by +1 for a common year, +2 for a leap year.
1965→66: +1 (Wed)
1966→67: +1 (Thu)
1967→68: +1 (Fri)
1968 is leap ⇒ 1968→69: +2 (Sun)
1969→70: +1 (Mon)
1970→71: +1 (Tue)
So next Tuesday falls on **5 Jan 1971**.