In the year whose January page is shown, how many months have both five Saturdays and five Sundays?

Five Saturdays AND five Sundays need Saturday and Sunday among the first (length − 28) days: a 30- or 31-day month starting on Saturday, or a 31-day month starting on Friday. 2031 (ordinary, starts Wed) month starts: Jan Wed, Feb Sat (28 days), Mar Sat (31), Apr Tue, May Thu, Jun Sun (30), Jul Tue, Aug Fri (31), Sep Mon, Oct Wed, Nov Sat (30), Dec Mon. That gives March, August and November: 3. (4 adds June, but a 30-day month from Sunday has only four Saturdays; 2 forgets that a 30-day month from Saturday qualifies.)