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Difficulty: MediumClocks and Calendars

A maritime shipping contract was enacted on Wednesday, October 14, 1795. The agreement stipulated a mandatory review and renegotiation exactly 14 years later, on October 14, 1809. On what day of the week did the renegotiation fall?

  1. A
    Friday
  2. B
    Sunday
  3. SaturdayAnswer
  4. D
    Wednesday

Answer

Saturday
The interval is exactly 14 years. Within this period, there are 3 leap years: 1796, 1804, and 1808. The year 1800 is a century year not divisible by 400, so it is not a leap year. This creates a total of 14 + 3 = 17 odd days. Dividing 17 by 7 gives a remainder of 3. Advancing 3 days from Wednesday results in Saturday.

Step-by-Step Solution

1
Calculate the total number of years elapsed between the two dates.
1809 - 1795 = 14 years.
Each normal year contributes 1 odd day, so determining the year gap gives the base number of odd days.
2
Identify the number of leap years occurring strictly within this 14-year period.
The leap years are 1796, 1804, and 1808. The year 1800 is not a leap year. Total = 3 leap years.
Century years (ending in 00) must be divisible by 400 to be leap years. Each valid leap year adds 1 additional odd day.
3
Calculate the total number of odd days.
14 (base odd days) + 3 (additional leap year days) = 17 total odd days.
Combining base year odd days with extra leap year odd days yields the complete shift in the weekly cycle.
4
Find the remainder when the total odd days are divided by 7, and add it to the starting day.
17 divided by 7 leaves a remainder of 3. Wednesday + 3 days = Saturday.
The days of the week repeat on a 7-day cycle, so only the remainder affects the final day.

Key Concept

Calculating odd days across century boundaries and identifying century leap years.
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Topics

Clocks and Calendars

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