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Difficulty: MediumClocks and Calendars

If January 15, 1894 fell on a Monday, what day of the week was January 15, 1904?

Answer: Friday / friday / FRIDAY

Answer

Friday
The period from January 15, 1894 to January 15, 1904 covers exactly 10 years. Within this period, we must count how many times February 29th is crossed. The year 1896 contributes one extra day. The year 1900 is a century year not divisible by 400, so it is a common year and contributes no extra days. The year 1904 is a leap year, but because the end date is January 15, we do not cross its February 29th, so it also contributes no extra days to this interval. The total number of odd days is 10 (for the 10 years) + 1 (for 1896) = 11. Dividing 11 by 7 leaves a remainder of 4. Four days after Monday is Friday.

Step-by-Step Solution

1
Determine the total number of years between the two dates.
The interval from January 15, 1894 to January 15, 1904 is exactly 10 years.
This provides the base number of odd days, as each standard 365-day year shifts the day of the week by 1.
2
Identify the leap years that contribute an extra day (February 29) strictly within this interval.
The only leap year whose February 29th is crossed is 1896.
The year 1896 is a regular leap year. The year 1900 is a century year not divisible by 400, so it is NOT a leap year. The year 1904 is a leap year, but the target date is January 15, meaning its February 29th has not yet occurred.
3
Calculate the total number of odd days.
10 (base years) + 1 (extra day for crossing February 29, 1896) = 11 odd days.
We add one extra day for each leap year February actually experienced in the given time window.
4
Determine the remainder when dividing the total odd days by 7.
11 divided by 7 leaves a remainder of 4.
The days of the week repeat in a standard 7-day cycle, so we use modulo 7 arithmetic.
5
Add the remainder to the starting day of the week.
Monday + 4 days = Friday.
Counting forward four days from Monday gives Tuesday, Wednesday, Thursday, and finally Friday.

Key Concept

Calculating odd days across a century boundary and evaluating leap year inclusion based on the month.

Alternative Method

You can count the shift year by year: 1894 to 1895 (+1), '95 to '96 (+1), '96 to '97 (+2, crosses Feb '96), '97 to '98 (+1), '98 to '99 (+1), '99 to 1900 (+1), 1900 to '01 (+1), '01 to '02 (+1), '02 to '03 (+1), '03 to 1904 (+1, stops in Jan). The total is 11, giving a net shift of 4 days.
Estimated Time:1m 0s
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Clocks and Calendars

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