Questions & Answers: "Calendar"

To find the day on 1st February 2010, given that 1st February 2016 was Monday, we need to calculate the total number of days between these two dates and then find the number of odd days. We will count the days from 1st February 2010 to 1st February 2016.

The period spans 6 years: 2010, 2011, 2012, 2013, 2014, 2015. We are looking at the interval from 1st Feb of the starting year to 1st Feb of the ending year.

1. Count normal years and leap years:

   • A normal year has 365 days.
   • A leap year has 366 days (due to February 29th).

   The leap year in this period is 2012. The 29th of February 2012 falls within the period from 1st February 2012 to 1st February 2013, so it adds an extra day. The year 2016 is a leap year, but its February 29th falls after 1st February 2016, so it does not affect the count for the interval ending on 1st February 2016.

   • Years considered as normal years (365 days): 2010, 2011, 2013, 2014, 2015 (5 years).
   • Year considered as a leap year (366 days): 2012 (1 year).

2. Calculate the total number of days: Total days = (Number of normal years × 365) + (Number of leap years × 366) Total days = (5 × 365) + (1 × 366) Total days = 1825 + 366 Total days = 2191 days.

3. Calculate the number of odd days: Odd days are the remainder when the total number of days is divided by 7 (since there are 7 days in a week). Odd days = 2191 ÷ 7 2191 = 7 × 313 + 0 So, the number of odd days is 0.

4. Determine the day of the week: Since the number of odd days is 0, it means that the day of the week repeats exactly after this period. We are going backward from 1st February 2016 to 1st February 2010. If 1st February 2016 was Monday, and there are 0 odd days when going backward, then 1st February 2010 must also be Monday.

Therefore, 1st February 2010 was a Monday.

To determine the day of the week for Education Day (November 11th, 2022), we need to calculate the number of days between Balika Din (January 24th, 2022) and Education Day.

First, let's calculate the remaining days in January: 31 (total days in January) - 24 (day of Balika Din) = 7 days.

Next, we add the number of days in the following months:

• February: 28 days (2022 was not a leap year)
• March: 31 days
• April: 30 days
• May: 31 days
• June: 30 days
• July: 31 days
• August: 31 days
• September: 30 days
• October: 31 days

Total days from January 24th to November 10th: 7 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 = 279 days.

Adding one more day for November 11th gives us a total of 280 days.

Now we divide the total number of days by 7 (days in a week) to find the remainder: 280 / 7 = 40 with a remainder of 0.

A remainder of 0 indicates that Education Day falls on the same day of the week as Balika Din. Since Balika Din (January 24th, 2022) was a Monday, Education Day (November 11th, 2022) was also a Monday.

To solve this, we must first determine if the year is a leap year. 2024 is divisible by 4, making it a leap year, which contains 366 days. In a leap year, the calendar shifts forward by 2 days from the start of the year to the start of the next year (since 366 divided by 7 leaves a remainder of 2). Therefore, Monday + 2 days = Wednesday. Tuesday is incorrect because that would be the shift for an ordinary year (365 days). Thursday is incorrect as it assumes a 3-day shift, and Monday is incorrect as it assumes no shift at all.

In a month of 31 days, the days that fall on the 1st, 2nd, and 3rd of the month appear 5 times. If the 3rd is a Tuesday, then the 2nd is a Monday and the 1st is a Sunday. Therefore, Sunday, Monday, and Tuesday will all appear 5 times in this month. Looking at the options, only Sunday is listed. Wednesday, Thursday, and Friday will only occur 4 times because they do not fall on the 1st, 2nd, or 3rd of this specific month.

We calculate the total number of days between the two dates: Remaining days in January = 5 (31 - 26); February = 28 (non-leap year); March = 31; April = 14. Total days = 5 + 28 + 31 + 14 = 78 days. Now, divide 78 by 7 to find the remainder: 78 ÷ 7 = 11 weeks and 1 remainder day. Since the remainder is 1, we move 1 day forward from Friday. Friday + 1 day = Saturday. Friday is wrong because it implies a remainder of 0; Sunday and Monday are wrong because they imply remainders of 2 and 3 respectively.

A normal year has 365 days. A leap year occurs approximately every four years to keep the calendar year synchronized with the astronomical year or seasonal year. In a leap year, the month of February has 29 days instead of its usual 28 days, adding one extra day to the year. Therefore, a leap year has $365 + 1 = 366$ days.

To find the day of the week, first calculate the number of days between 10th March and 25th March. $25 - 10 = 15$ days. Since the days of the week repeat every 7 days, we divide the total number of days by 7 and find the remainder. $15 \div 7 = 2$ with a remainder of $1$. This means the day will be 1 day after Tuesday. Tuesday + 1 day = Wednesday. Wait, I made a mistake in my thought process. $15 \div 7 = 2$ remainder $1$. So it should be Tuesday + 1 day = Wednesday. Let me re-evaluate. Let's count: 10th (Tuesday), 11th (Wednesday), 12th (Thursday), 13th (Friday), 14th (Saturday), 15th (Sunday), 16th (Monday), 17th (Tuesday), 18th (Wednesday), 19th (Thursday), 20th (Friday), 21st (Saturday), 22nd (Sunday), 23rd (Monday), 24th (Tuesday), 25th (Wednesday). Ah, the calculation of 'number of days between' should be inclusive of the end date, or exclusive of the start date if considering 'days after'. If we count 'days after 10th March until 25th March', it's 15 days forward. If 10th is Tuesday, then 10+7 = 17th is Tuesday. 17+7 = 24th is Tuesday. So, 25th must be Wednesday. My initial option was wrong. I must correct the options or my calculation. Let's make the correct option as Wednesday and fix the JSON.

Corrected explanation: To find the day of the week, first calculate the number of days from 10th March to 25th March, inclusive of 25th March. The number of days is $25 - 10 = 15$. Since the days of the week repeat every 7 days, we divide the total number of days by 7 and find the remainder. $15 \div 7 = 2$ with a remainder of $1$. This means the day will be 1 day after Tuesday. Counting forward 1 day from Tuesday, we get Wednesday. Therefore, 25th March will be a Wednesday.

To find the day of the week for 1st August, we need to calculate the total number of days from 1st June to 1st August. \n\nNumber of days in June (after 1st June): June has 30 days. So, from 2nd June to 30th June, there are $30 - 1 = 29$ days.\nNumber of days in July: July has 31 days.\nNumber of days in August (up to 1st August): There is 1 day.\n\nTotal number of days $= 29 + 31 + 1 = 61$ days.\n\nNow, we divide the total number of days by 7 to find the remainder, which tells us how many days forward we need to count from the starting day (Saturday). $61 \div 7 = 8$ with a remainder of $5$. \n\nSo, we need to count 5 days forward from Saturday:\nSaturday + 1 day = Sunday\nSaturday + 2 days = Monday\nSaturday + 3 days = Tuesday\nSaturday + 4 days = Wednesday\nSaturday + 5 days = Thursday\n\nTherefore, 1st August will fall on a Thursday.