019.js

// You are given the following information, but you may prefer to do some
// research for yourself.
//
//   * 1 Jan 1900 was a Monday.

//   * Thirty days has September,
//     April, June and November.
//     All the rest have thirty-one,
//     Saving February alone,
//     Which has twenty-eight, rain or shine.
//     And on leap years, twenty-nine.

//   * A leap year occurs on any year evenly divisible by 4, but not on a
// century unless it is divisible by 400.
//
// How many Sundays fell on the first of the month during the twentieth century
// (1 Jan 1901 to 31 Dec 2000)?

function monthdays(month, year) {
    switch (month) {
        case 1:
        case 3:
        case 5:
        case 7:
        case 8:
        case 10:
        case 12:
            return 31;
            break;
        case 4:
        case 6:
        case 9:
        case 11:
            return 30;
            break;
        case 2:
            return (year%4 === 0 && (year%100 !== 0 || year%400 === 0)) ? 29 : 28;
            break;
        default:
            break;
    }
}

function howManySundays(startYear, endYear) {
    var sundays = 0;
    var day = 1;// 1 Jan 1900
    for (var y = 1900; y <= endYear; y++) {
        for (var m = 1; m <= 12; m++) {
            day = (day + monthdays(m, y) - 1)%7 + 1;
            if (y < startYear) continue;
            if (day === 7) {
                sundays++;
            }
        }
    }
    return sundays;
}

console.log( howManySundays(1901, 2000) );