Introduction / Context:
This calendar problem gives a weekday for 9 July 2013 and asks for the weekday on 7 January 2014. Instead of using real life calendar data, the question asks you to work logically from the given assumption. The key idea is to count the number of days between the two dates, reduce that number modulo 7, and then use the fixed weekly cycle to shift the weekday appropriately.
Given Data / Assumptions:
- 9 July 2013 is given as a Sunday.
- We need the day of the week on 7 January 2014.
- Year 2013 is a non leap year.
- We assume the Gregorian calendar.
Concept / Approach:
We count the total number of days from 9 July 2013 to 7 January 2014. Then we compute the remainder when that total is divided by 7 to determine how many steps forward in the weekday cycle we move. If the total number of days is a multiple of 7, then the weekday will be the same. Since we are using the given assumption that 9 July 2013 is a Sunday, we treat it as our starting point without worrying about whether that matches real world history.
Step-by-Step Solution:
Compute days remaining in July 2013 after 9 July.
July has 31 days, so remaining days from 10 July to 31 July = 31 - 9 = 22 days.
Months from August 2013 to December 2013 contribute:
August: 31, September: 30, October: 31, November: 30, December: 31.
Total for August to December = 31 + 30 + 31 + 30 + 31 = 153 days.
Days from 1 January 2014 to 7 January 2014 inclusive = 7 days.
Total days between 9 July 2013 and 7 January 2014 = 22 + 153 + 7 = 182 days.
Compute 182 modulo 7: 182 = 7 * 26, so remainder is 0.
With 0 odd days, the weekday on 7 January 2014 is the same as on 9 July 2013, which is Sunday.
Verification / Alternative check:
Observe that 182 days equal exactly 26 weeks.
Since the number of full weeks between the two dates is an integer, we return to the same weekday.
Therefore, the conclusion that both dates are Sundays is consistent.
Why Other Options Are Wrong:
Option B (Saturday), Option C (Monday), and Option D (Friday) all imply a non zero remainder when days are divided by 7, which is not the case.
Option A (Sunday): Correct because 26 complete weeks pass between the two dates with no extra days.
Common Pitfalls:
Miscounting the days left in July or the total days in the remaining months can change the total and lead to the wrong weekday.
Some learners forget that inclusive and exclusive counting conventions matter; here we count full days between the two dates.
Another common mistake is to try to use real calendar knowledge to override the assumption given in the problem, which is not needed.
Final Answer:
7 January 2014 falls on a Sunday under the given assumption.
Discussion & Comments