Understanding the Calendar Problem

This question asks us to find the day of the week on a specific date in the future, given the day on an earlier date. The key to solving such problems in calendars is understanding the concept of 'odd days'.

An ordinary year has 365 days, and a leap year has 366 days. When we divide the number of days in a year by 7 (the number of days in a week), the remainder is the number of odd days.

• A normal year has 365 days. \(365 \div 7 = 52\) weeks and 1 day remaining. So, a normal year has 1 odd day.
• A leap year has 366 days. \(366 \div 7 = 52\) weeks and 2 days remaining. So, a leap year has 2 odd days.

The day of the week advances by the number of odd days when we move from one date to the same date in the next year (or across a period).

Calculating Odd Days Between 18th February 1997 and 18th February 1999

We need to find the number of odd days between 18th February 1997 and 18th February 1999.

This period covers two full years: from 18th February 1997 to 18th February 1998, and from 18th February 1998 to 18th February 1999.

Checking for Leap Years

We need to determine if the years 1997, 1998, and 1999 are leap years to calculate the number of odd days correctly. A year is a leap year if it is divisible by 4, except for years divisible by 100 but not by 400.

• 1997: \(1997 \div 4\) is not an integer. 1997 is a normal year.
• 1998: \(1998 \div 4\) is not an integer. 1998 is a normal year.
• 1999: \(1999 \div 4\) is not an integer. 1999 is a normal year.

Neither 1997, 1998, nor 1999 is a leap year. Importantly, the period from Feb 18, 1997, to Feb 18, 1999, includes the full calendar year 1998. Since 1998 is a normal year, the leap day (February 29th) does not occur within the years covered in this span.

Calculating Total Odd Days

• From 18th February 1997 to 18th February 1998: This span is exactly one year. Since 1997 is a normal year, there is 1 odd day.
• From 18th February 1998 to 18th February 1999: This span is exactly one year. Since 1998 is a normal year, there is 1 odd day.

Total odd days from 18th February 1997 to 18th February 1999 = Number of odd days (1997-1998) + Number of odd days (1998-1999) = \(1 + 1 = 2\) odd days.

Determining the Day on 18th February 1999

The day of the week on 18th February 1997 was Tuesday.

We have a total of 2 odd days between 18th February 1997 and 18th February 1999. This means the day of the week will advance by 2 days from Tuesday.

• Tuesday + 1 day = Wednesday
• Wednesday + 1 day = Thursday

Therefore, the day on 18th February 1999 was Thursday.

Summary of Calculation

Starting Day: Tuesday (18th February 1997)

Number of years: 2 (1997-1998 and 1998-1999)

Leap years in the period (crossing Feb 29th): None

Odd days per year: 1 for a normal year

Total odd days: \(1 \text{ (for 1997-1998)} + 1 \text{ (for 1998-1999)} = 2\)

Final Day: Tuesday + 2 days = Thursday

Revision Table: Odd Days in Calendar Calculations

Additional Information on Calendar Concepts

Understanding the calendar structure is crucial for these problems. Here are some key points:

• Normal Year: A year with 365 days. The same date in the next year will be one day ahead (e.g., if Jan 1, 2023, was Sunday, Jan 1, 2024, was Monday).
• Leap Year: A year with 366 days, including February 29th. This occurs every four years, except for years divisible by 100 unless they are also divisible by 400. Examples: 2000 was a leap year (divisible by 400), 1900 was not (divisible by 100 but not 400), 2024 is a leap year (divisible by 4).
• Effect of Leap Year: If February 29th is included in the period you are counting, it adds an extra day, resulting in 2 odd days for that year instead of 1. For example, from March 1, 2023, to March 1, 2024 (a leap year), the day will shift by 2 days because Feb 29, 2024 is included. However, from Jan 1, 2024, to Jan 1, 2025, the shift is only 1 day, as Feb 29, 2024, falls within the first year but doesn't affect the step exactly one year later. In our problem (Feb 18, 1997 to Feb 18, 1999), we are counting the full years 1997-1998 and 1998-1999. Neither 1997 nor 1998 is a leap year, so Feb 29 is not included in either yearly span.
• Calculating Day Shift: For every odd day, the day of the week moves forward by one day. If you have 'n' odd days, the day moves forward by 'n' days. If 'n' is greater than 7, you take the remainder when 'n' is divided by 7 to find the final shift (e.g., 8 odd days is same as 1 odd day shift, \(8 \div 7 = 1\) R 1).

In this specific problem, since we moved from Feb 18, 1997, to Feb 18, 1999, spanning two normal years, we added 1 odd day for each year, totaling 2 odd days. Starting from Tuesday, adding 2 days leads us to Thursday.