In the year of these two leaves, 1 January and 31 December fall on the same weekday. In which later year will both these days fall on a Thursday?

1 January and 31 December share a weekday only in an ordinary year (364 days apart). So we need an ordinary year starting on Thursday. 1 January: 2032 Thu (but 2032 is a leap year, so 31 December 2032 is a Friday), 2033 Sat, 2034 Sun, 2035 Mon, 2036 Tue (leap), 2037 Thu, and 2037 is ordinary. (2032 is the leap-year trap.)