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Question

Difficulty: MediumClocks and Calendars

A scientist was born on February 29, 2096, which happens to be a Wednesday. Because of the specific rules governing the Gregorian calendar, they only celebrate their birthday on the exact date of February 29. On what day of the week will they celebrate their first actual birthday?

  1. FridayAnswer
  2. B
    Monday
  3. C
    Thursday
  4. D
    Saturday

Answer

Friday
The next leap year after 2096 is 2104, making an 8-year gap because 2100 is an ordinary year. This 8-year interval consists of 7 ordinary years and 1 leap year. Calculating the odd days yields (7 × 1) + (1 × 2) = 9 odd days. Dividing 9 by 7 gives a remainder of 2. Adding 2 days to Wednesday results in Friday.

Step-by-Step Solution

1
Determine the year of the first actual birthday.
February 29, 2104.
The year 2100 is a century year not divisible by 400, making it a common year. The next leap year containing February 29 after 2096 is 2104.
2
Calculate the total number of years and identify leap years in the interval.
8 years total, consisting of 7 ordinary years and 1 leap year (2104).
The period from February 29, 2096, to February 29, 2104, spans exactly 8 years. Only 2104 contributes a February 29th at the end of its respective annual cycle within this specific gap.
3
Calculate the total number of odd days.
9 odd days.
The 7 ordinary years contribute 1 odd day each (7), and the 1 leap year contributes 2 odd days. Total = 7 + 2 = 9.
4
Determine the final day of the week.
Friday.
9 days divided by 7 leaves a remainder of 2 odd days. Adding 2 days to the starting day of Wednesday results in Friday.

Key Concept

Leap year identification across century boundaries and odd day calculation.
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Topics

Clocks and Calendars

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