Calculating the Day of the Week for 5 February 2008

Finding the day of the week for a specific date like 5 February 2008 is a common type of calendar problem. These problems can be solved using various methods, often involving the concept of 'odd days'. The odd day method helps us determine the number of days in excess of a complete week.

To find the day of the week for 5 February 2008, we can calculate the total number of odd days from a reference point up to the given date. A convenient reference point is often the start of a century or a known base year like 2000.

Understanding Odd Days

An ordinary year has 365 days. $365 \div 7 = 52$ weeks and 1 day. So, an ordinary year has 1 odd day.

A leap year has 366 days. $366 \div 7 = 52$ weeks and 2 days. So, a leap year has 2 odd days.

The number of odd days in a month depends on the number of days in the month:

• Months with 31 days (Jan, Mar, May, Jul, Aug, Oct, Dec): $31 \div 7 = 4$ weeks and 3 days. 3 odd days.
• Months with 30 days (Apr, Jun, Sep, Nov): $30 \div 7 = 4$ weeks and 2 days. 2 odd days.
• February: 28 days in ordinary year ($28 \div 7 = 4$ weeks, 0 odd days), 29 days in leap year ($29 \div 7 = 4$ weeks and 1 day, 1 odd day).

Calculating Odd Days for 5 February 2008

We need to calculate the total odd days until 5 February 2008. We can break this down:

1. Odd days in completed years up to the end of 2007.
2. Odd days in the year 2008 until 5 February.

1. Odd Days in Completed Years (Up to the end of 2007)

Let's calculate odd days from the year 2000, as it's a leap century year (divisible by 400), and the number of odd days in 400 years is 0. So, odd days up to 2000 = 0.

We need to find the odd days in the years 2001 to 2007 (7 years).

We need to identify the number of leap years and ordinary years in this period (2001-2007).

• A year is a leap year if it is divisible by 4, unless it is a century year not divisible by 400.
• In the years 2001, 2002, 2003, 2004, 2005, 2006, 2007, the only year divisible by 4 is 2004.
• So, there is 1 leap year (2004) and $7 - 1 = 6$ ordinary years.

Total odd days in these 7 years:

• Odd days in 6 ordinary years = $6 \times 1 = 6$
• Odd days in 1 leap year = $1 \times 2 = 2$
• Total odd days from 2001 to 2007 = $6 + 2 = 8$

Total odd days up to the end of 2007 = Odd days up to 2000 + Odd days from 2001 to 2007 = $0 + 8 = 8$.

We take the remainder when divided by 7: $8 \div 7 = 1$ week and 1 day. So, 1 odd day.

Odd days up to the end of 2007 = 1.

2. Odd Days in the Year 2008 (Until 5 February)

The year 2008 is divisible by 4, so it is a leap year. February 2008 has 29 days.

We need to count the odd days from the beginning of 2008 until 5 February:

• January 2008: 31 days. Odd days = $31 \pmod{7} = 3$.
• February 2008: Up to 5th day. Odd days = 5.

Total odd days in 2008 until 5 February = $3 + 5 = 8$.

We take the remainder when divided by 7: $8 \pmod{7} = 1$.

Odd days in 2008 until 5 February = 1.

3. Total Odd Days and Determining the Day

Total odd days until 5 February 2008 = Odd days up to end of 2007 + Odd days in 2008 until 5 Feb.

Total odd days = $1 + 1 = 2$.

Now we map the total number of odd days to the day of the week. A common convention for this method is:

Since the total number of odd days is 2, the day of the week for 5 February 2008 is Tuesday.

Summary of Calculation

• Odd days up to end of 2007: 1
• Odd days from Jan 1, 2008 to Feb 5, 2008: 1 (Jan: 3 odd days; Feb: 5 days. Total 8 odd days, $8 \pmod{7} = 1$)
• Total odd days = $1 + 1 = 2$
• Mapping 2 odd days corresponds to Tuesday.

Revision Table: Key Concepts for Calendar Problems

Additional Information: Calendar Odd Day Method

The odd day method is a powerful technique for solving calendar-based reasoning problems. It relies on the fact that the day of the week repeats every 7 days. By calculating the total number of days from a known point in time and finding the remainder when divided by 7, we can determine the day of the week for any given date.

The base day convention (which day corresponds to 0 odd days) can vary, but the method of calculating odd days remains consistent. The key is accurately accounting for leap years, as they add an extra day (and thus an extra odd day) in February.

Leap years occur every 4 years, except for century years unless they are divisible by 400. So, 1900 was not a leap year (divisible by 100 but not 400), but 2000 was a leap year (divisible by 400).

This method is widely used in aptitude tests and competitive exams to quickly solve date-related questions.