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Problem 19

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Counting Sundays

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 $2000$)?

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周日计数

下列信息是已知的，当然你也不妨自己再验证一下：

• $1900$年$1$月$1$日是周一。
• 三十天在九月中，
  四六十一也相同。
  剩下都是三十一，
  除去二月不统一。
  二十八天平常年，
  多加一天在闰年。
• 闰年指的是能够被$4$整除却不能被$100$整除，或者能够被$400$整除的年份。

在二十世纪（$1901$年$1$月$1$日到$2000$年$12$月$31$日）中，有多少个月的$1$号是周日？

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