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Question

Difficulty: MediumClocks and Calendars

A university establishes a new scholarship fund on September 15, 2195, which happens to be a Friday. The founding document states that a major administrative review of the fund will occur exactly 1212 years later on September 15, 2207. What day of the week will this review take place?

Answer: Friday / friday / FRIDAY

Answer

Friday
The 1212-year period from 2195 to 2207 contains only 22 leap years (2196 and 2204). The year 2200 is a century year not divisible by 400400, meaning it is a common year with 365365 days. The total shift in days of the week is equal to the number of years (1212) plus the number of extra leap days (22), resulting in a total shift of 1414 days. Since 1414 is a perfect multiple of 77, there are 00 odd days. The day of the week shifts by exactly 00 days, meaning the review will also take place on a Friday.

Step-by-Step Solution

1
Identify the total number of years in the given interval.
From 2195 to 2207 is exactly 1212 years.
This sets the baseline shift, as every standard year shifts the calendar by at least 11 day.
2
Determine the number of leap years in this 12-year interval.
The years divisible by 44 in this range are 2196, 2200, and 2204. However, century years are only leap years if divisible by 400400. Since 2200 is not divisible by 400400, it is not a leap year. Thus, there are only 22 leap years: 2196 and 2204.
Each leap year adds an additional 11 day to the shift because it has 366366 days instead of 365365.
3
Calculate the total number of odd days (total shift in days of the week).
Each normal year contributes 11 odd day, and each leap year contributes 22 odd days. For 1212 years with 22 leap years, the easiest calculation is: 1212 (one for each year) +2+ 2 (extra day for each leap year) =14= 14 days.
This gives the absolute number of days the weekday will advance.
4
Determine the final day of the week.
A shift of 1414 days is exactly 22 full weeks (1414 divided by 77 leaves a remainder of 00). Therefore, the day of the week remains the same. Friday +0+ 0 days == Friday.
Days of the week repeat every 77 days, so we use modulo 77 arithmetic.

Key Concept

Calculating day of the week shifts across century boundaries, accounting for the rule that non-400 century years are not leap years.
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Topics

Clocks and Calendars

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