Problem 19
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)?
# 计算1901.1.1到2000.12.31一共有多少个星期日是月初第一天。
def leap_year(n): if n % 400 == 0 or (n % 100 != 0 and n % 4 == 0): return True return False month_days = [31,28,31,30,31,30,31,31,30,31,30,31] days = 365 # From 1901 count = 0 for year in range(1901,2001): if leap_year(year): month_days[1] = 29 for month in range(12): days += month_days[month] if days % 7 == 6: count += 1 print(count-1) # 2001 1.1 is Sunday
结果:171
当然比较简单的思路就是月初第一天是星期几的概率是一样的,所以 1200/7 = 171...3 答案就是171或172