It was Monday on 1st January 2018. What was the day of the week on 1st January 2010?

Options

A. Tuesday
B. Thursday
C. Friday
D. Monday

Answer

To determine the day of the week on January 1, 2010, given that January 1, 2018, is a Monday, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the years to consider**: We need to find the day of the week for January 1, 2010, while we know January 1, 2018, is a Monday.

2. **Count the years backwards**: We will count backwards from 2018 to 2010, which includes the years 2017, 2016, 2015, 2014, and 2013, and so on.

3. **Determine if each year is a leap year or a common year**:
- A common year has 365 days, which means it adds 1 day to the week.
- A leap year has 366 days, which means it adds 2 days to the week.

4. **Identify leap years between 2010 and 2018**:
- The leap years are 2012 and 2016.

5. **Calculate the total day shifts**:
- From 2018 to 2017 (common year): +1 day
- From 2017 to 2016 (leap year): +2 days
- From 2016 to 2015 (common year): +1 day
- From 2015 to 2014 (common year): +1 day
- From 2014 to 2013 (common year): +1 day
- From 2013 to 2012 (leap year): +2 days
- From 2012 to 2011 (common year): +1 day
- From 2011 to 2010 (common year): +1 day

6. **Sum the total shifts**:
- Total shifts = 1 (2017) + 2 (2016) + 1 (2015) + 1 (2014) + 1 (2013) + 2 (2012) + 1 (2011) + 1 (2010) = 10 days.

7. **Determine the day of the week**:
- Since January 1, 2018, is a Monday, we subtract the total shifts (10 days) from Monday.
- 10 days mod 7 = 3 (because 10 divided by 7 gives a remainder of 3).
- Counting backwards from Monday:
- 1 day back: Sunday
- 2 days back: Saturday
- 3 days back: Friday

Thus, January 1, 2010, was a **Friday**.