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A multinational corporation signed a 100100-year lease for its global headquarters on Monday, May 18, 2026. The lease agreement explicitly states that it will expire on exactly the same date 100100 years later, on May 18, 2126. On what day of the week will this lease expire?

  1. SaturdayCevap
  2. B
    Sunday
  3. C
    Wednesday
  4. D
    Friday

Cevap

Saturday
The interval between May 18, 2026, and May 18, 2126 is exactly 100100 years. Normally, a 100100-year span contains 2525 leap years, but because the year 21002100 is a century year not divisible by 400400, it is not a leap year. This leaves exactly 2424 leap years in the period. The total number of odd days is the sum of ordinary years and leap year extras: 100+24=124100 + 24 = 124 odd days. When dividing 124124 by 77, the remainder is 55. Advancing 55 days from Monday results in Saturday.

Adım Adım Çözüm

1
Calculate the total number of years in the given timeframe.
The period from May 18, 2026 to May 18, 2126 is exactly 100100 years.
This establishes the base number of odd days, as every ordinary year contributes exactly 11 odd day.
2
Determine the number of leap years within this 100-year interval.
There are 2424 leap years.
Normally, a 100100-year span contains 2525 leap years (100÷4=25100 \div 4 = 25). However, the span crosses the year 21002100. Because 21002100 is a century year but is not divisible by 400400, it is not a leap year. Therefore, we subtract 11 from 2525 to get 2424 leap years.
3
Calculate the total number of odd days accumulated over the 100 years.
The total is 124124 odd days.
Each of the 100100 years contributes 11 base odd day (100100 days), and each of the 2424 leap years contributes an additional odd day (2424 days). 100+24=124100 + 24 = 124.
4
Find the final day of the week by evaluating the total odd days modulo 7.
The remainder is 55, which shifts the day from Monday to Saturday.
124÷7=17124 \div 7 = 17 weeks with a remainder of 55 days. Counting 55 days forward from Monday gives Saturday.

Anahtar Kavram

Calculating odd days over a multi-year period while correctly applying the century non-leap year rule.
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