Math Problem Statement

If 10 October 2003 was a Friday, then what was the day of the week on 8 October 2015?

Solution

To determine the day of the week on 8 October 2015, given that 10 October 2003 was a Friday, we will count the number of days between the two dates and calculate the remainder when divided by 7 (since there are 7 days in a week).

Step-by-step process:

  1. From 10 October 2003 to 10 October 2015:

    • From 2003 to 2015, there are 12 years.
    • In these 12 years, there are leap years and non-leap years:
      • Leap years (366 days): 2004, 2008, 2012 (3 leap years).
      • Non-leap years (365 days): 2003, 2005, 2006, 2007, 2009, 2010, 2011, 2013, 2014, 2015 (9 non-leap years).
  2. Total days between 10 October 2003 and 10 October 2015:

    • Leap years: 3×366=10983 \times 366 = 1098 days
    • Non-leap years: 9×365=32859 \times 365 = 3285 days
    • Total days = 1098+3285=43831098 + 3285 = 4383 days
  3. Adjust for the difference between 8 October 2015 and 10 October 2015:

    • 8 October is 2 days earlier than 10 October, so we subtract 2 days: 43832=43814383 - 2 = 4381 days.
  4. Determine the day of the week:

    • We divide the total number of days by 7 to find the remainder: 4381÷7=626 remainder 34381 \div 7 = 626 \text{ remainder } 3
    • This remainder of 3 means that 8 October 2015 is 3 days later than a Friday.

Therefore, 8 October 2015 was a Monday.

Would you like further clarification or details on this?


Here are some related questions to expand your understanding:

  1. How do leap years affect the day of the week in the long term?
  2. What is the difference between the Julian and Gregorian calendars in terms of leap years?
  3. How would you calculate the day of the week for dates far in the future or past?
  4. How do you calculate the day of the week using Zeller's Congruence?
  5. How does the addition of a leap day every 4 years impact the calculation of days?

Tip: Always remember that leap years occur every 4 years, except for years divisible by 100 but not 400!

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Math Problem Analysis

Mathematical Concepts

Calendar Calculations
Day of the Week Determination
Leap Year Counting

Formulas

Days Calculation Formula
Modulo Operation for Day Calculation

Theorems

Leap Year Rule
Modulo Arithmetic

Suitable Grade Level

Grades 8-10