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A prominent industrial facility was inaugurated on March 1515, 18971897, which happened to be a Monday. The facility's operational license mandated a comprehensive structural safety inspection exactly 1010 years later on the exact same date. What day of the week was the inspection scheduled for?

  1. A
    Thursday
  2. B
    Saturday
  3. FridayCevap
  4. D
    Sunday

Cevap

The inspection was scheduled for Friday.
Between 18971897 and 19071907, a span of 1010 years elapses, producing a baseline of 1010 odd days. It is critical to recognize that the year 19001900, despite being a multiple of 44, is a century year not divisible by 400400, and therefore is not a leap year. The only leap year in this timeframe is 19041904. Adding this 11 extra odd day gives a total of 1111 odd days. Dividing 1111 by 77 yields a remainder of 44. Advancing 44 days forward from Monday gives Friday.

Adım Adım Çözüm

1
Determine the total interval of years between the start and end dates.
The period from March 1515, 18971897 to March 1515, 19071907 is exactly 1010 years.
Every standard year provides 11 odd day, giving a baseline of 1010 odd days.
2
Identify the number of leap years within this specific 1010-year interval.
The only leap year crossed is 19041904. The year 19001900 is a century year not divisible by 400400, meaning it is a standard year of 365365 days.
Leap years contain 366366 days and contribute an extra odd day. Century years follow a different mathematical rule for leap year designation.
3
Calculate the total number of odd days accrued over the period.
1010 baseline odd days + 11 extra odd day (for the leap year 19041904) = 1111 total odd days.
Total odd days equal the number of years plus the number of leap years in the given interval.
4
Find the equivalent shift within a standard 77-day week.
11(mod7)=411 \pmod 7 = 4 odd days.
Because the days of the week cycle every 77 days, we only use the remainder to find the final day.
5
Add the calculated odd days to the initial day of the week.
Monday + 44 days = Friday.
Moving 44 days forward in the weekly cycle from Monday lands precisely on Friday.

Anahtar Kavram

Calculating odd days across calendar intervals containing non-leap century boundaries.
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Clocks and Calendars

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