The leaf shows 1 January 2001. Using odd days and the century rule for leap years, on which day of the week will 1 January 2201 fall?

2001–2200 is 200 years. Multiples of 4 from 2004 to 2200: 50, but 2100 and 2200 are not leap years (not divisible by 400), so 48 leap years. Odd days $=200+48=248=35\times 7+3$. Monday + 3 = Thursday. (Friday treats one of 2100 and 2200 as a leap year; Wednesday leaves out one leap year too many.)