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A rare astronomical alignment was recorded on Thursday, May 17, 1888. According to a research institute, this specific alignment occurs exactly every 13 years. On what day of the week will the second occurrence after the original 1888 recording take place?

  1. SundayCevap
  2. B
    Monday
  3. C
    Friday
  4. D
    Tuesday

Cevap

Sunday
The second occurrence takes place 26 years after 1888, in the year 1914. Between May 1888 and May 1914, there are 26 years, 5 of which are leap years (1892, 1896, 1904, 1908, 1912). The year 1900 is not a leap year. This gives 26 + 5 = 31 odd days. Since 31 divided by 7 leaves a remainder of 3, the event occurs 3 days after Thursday, which is Sunday.

Adım Adım Çözüm

1
Determine the target year for the second occurrence.
The interval is 13 years, so the second occurrence happens 2 × 13 = 26 years after the original recording. Target year is 1888 + 26 = 1914.
The question asks for the second occurrence, which requires adding two full intervals to the base year.
2
Calculate the total number of years and identify all leap years in the interval from May 17, 1888, to May 17, 1914.
Total years: 26. Leap years passed: 1892, 1896, 1904, 1908, 1912 (5 leap years). Note that 1900 is a century year not divisible by 400, so it is not a leap year.
To calculate the shift in the days of the week, we need the total number of normal years and leap years. Leap years add an extra odd day.
3
Calculate the total number of odd days over the 26-year period.
Total odd days = 26 + 5 = 31 odd days.
Each normal year contributes 1 odd day, and each leap year contributes an additional 1 odd day. Adding the number of leap years to the total number of years gives the total odd days.
4
Find the final day of the week by adding the remainder of odd days to the starting day.
31 divided by 7 leaves a remainder of 3. Three days after Thursday is Sunday.
The days of the week repeat every 7 days. Dividing the total odd days by 7 gives the effective shift.

Anahtar Kavram

Calculating odd days across a time interval that includes a century boundary to determine the day of the week.
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