public class Solution {
    public static void main(String[] args) {
        System.out.println(isDateOdd("JANUARY 2 2020"));
    }

    public static boolean isDateOdd(String date) {
        Date startyear = new Date();
        startyear.setHours(0);
        startyear.setMinutes(0);
        startyear.setSeconds(0);

        startyear.setDate(1);
        startyear.setMonth(0);

        Date newDate = new Date(date);
        long distance = newDate.getTime() - startyear.getTime();
        int sutki = 24 * 60 * 60 * 1000;
        int count = (int) (distance/sutki);

        if (count%2!=0) return true;
        else return false;
    }
}
Не проходит по третьему критерию.