Question

On which dates will Sundays come in February 2020?

• A. 3, 10, 17, 24 of February
• B. 8, 15, 22, 29 of February
• C. 2, 9, 16, 23 of February
• D. 5, 12, 19, 26 of February

Answer 1

Answer:

C. 2, 9, 16, 23 of February

## 1. Count the Odd Days up to the Year 2019

We break down the years from 1 AD to 2019 into centuries and remaining years:

* First 2000 years: 2000 is a multiple of 400. Every 400 years has 0 odd days.

* Next 19 years (2001 to 2019):

* Total normal days/years = 19

* Leap years in 19 years = $19 \div 4 = 4$ leap years.

* Total odd days = $19 + 4 = 23\text{ odd days}$.

* Simplify by dividing by 7: $23 \div 7 = 3$ weeks with a remainder of 2 odd days.

## 2. Count the Days in the Year 2020

We only need to count the days up to February 1st:

* January: 31 days. Simplify by dividing by 7: $31 \div 7 = 4$ weeks with a remainder of 3 odd days.

* February: We only need the 1st day = 1 odd day.

## 3. Add All the Odd Days Together

Add the remainders from all steps:

$2 \text{ (from 2019)} + 3 \text{ (from Jan)} + 1 \text{ (from Feb 1)} = \mathbf{6\text{ odd days}}$

## 4. Match the Remainder to the Day

In this system, days are numbered starting from Sunday (0) to Saturday (6):

* 0 = Sunday

* 1 = Monday

* 2 = Tuesday

* 3 = Wednesday

* 4 = Thursday

* 5 = Friday

* 6 = Saturday

Since our total remainder is 6, February 1, 2020, is mathematically proven to be a Saturday.

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In February 2020, Sundays fell on the following dates: 2, 9, 16, and 23.

## Breakdown:

The year 2020 was a leap year, meaning February had 29 days. According to the [February 2020 Calendar], the month started on a Saturday:

* February 1 – Saturday

* February 2 – First Sunday

* February 9 – Second Sunday

* February 16 – Third Sunday

* February 23 – Fourth Sunday

The remaining days after the 23rd were Monday (24th) through Saturday (29th), so there were only four Sundays in that month