Day Calculation: Jan 1, 2001 to Jan 26, 2003

We need to find the day of the week for 26^th January, 2003, given that 1^st January, 2001 was a Monday.

We can calculate the day shift year by year.

Finding the Day for Jan 1, 2002

The year 2001 has 365 days. Since 365 divided by 7 leaves a remainder of 1 ($365 \mod 7 = 1$), the day of the week shifts forward by 1 day each normal year.

Calculation:

• Number of days in 2001 = 365
• Remainder = $365 \div 7 = 52$ remainder 1
• Therefore, 1^st January, 2002 was a Monday + 1 day = Tuesday.

Finding the Day for Jan 1, 2003

The year 2002 also has 365 days (it's not a leap year). The day shifts forward by 1 day again.

Calculation:

• Number of days in 2002 = 365
• Remainder = $365 \div 7 = 52$ remainder 1
• Therefore, 1^st January, 2003 was a Tuesday + 1 day = Wednesday.

Finding the Day for Jan 26, 2003

We know that 1^st January, 2003 was a Wednesday. We need to find the day for 26^th January, 2003.

Calculate the number of days passed from 1^st January, 2003 to 26^th January, 2003.

Number of days = $26 - 1 = 25$ days.

Now, find the remainder when 25 is divided by 7.

Calculation:

• $25 \div 7 = 3$ remainder 4

This means the day of the week for 26^th January, 2003 will be 4 days after Wednesday.

• Wednesday + 1 day = Thursday
• Wednesday + 2 days = Friday
• Wednesday + 3 days = Saturday
• Wednesday + 4 days = Sunday

So, 26^th January, 2003 was a Sunday.

Final Answer Determination

Based on the calculation, the day on 26^th January, 2003 was Sunday.