Solving the Calendar Day Calculation Problem

This problem requires us to find the day of the week for a specific date (11 June 2019) based on the day of another date (11 January 2018).

The key to solving calendar problems like this is to calculate the total number of days between the two dates and then find 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). The number of odd days tells us how many days forward or backward we need to move from the starting day to find the day of the target date.

Step 1: Calculate the Number of Odd Days from 11 January 2018 to 11 January 2019

First, let's find the day for the same date in the following year. The period from 11 January 2018 to 11 January 2019 is exactly one year.

• The year 2018 is not a leap year (it's not divisible by 4).
• A normal year has 365 days.
• To find the number of odd days in a normal year, we divide 365 by 7:

$\frac{365}{7} = \frac{52 \times 7 + 1}{7} = 52 \text{ weeks } + 1 \text{ day}$

• The remainder is 1. So, there is 1 odd day in a normal year.
• If 11 January 2018 was a Thursday, then 11 January 2019 will be Thursday + 1 odd day.

Thursday + 1 day = Friday.

So, 11 January 2019 falls on a Friday.

Step 2: Calculate the Number of Odd Days from 11 January 2019 to 11 June 2019

Now, we need to find the number of odd days from 11 January 2019 to 11 June 2019. We'll calculate the number of days remaining in January 2019 and then add the number of days in the subsequent months up to 11 June 2019.

• Days remaining in January 2019 (from 11th): 31 - 11 = 20 days
• February 2019: 28 days (2019 is not a leap year)
• March 2019: 31 days
• April 2019: 30 days
• May 2019: 31 days
• Days in June 2019 (up to 11th): 11 days

Total number of days = 20 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31 (May) + 11 (Jun)

Total number of days = 151 days.

Now, let's find the odd days in these 151 days:

$\frac{151}{7}$

$151 = 7 \times 21 + 4$

The remainder is 4. So, there are 4 odd days between 11 January 2019 and 11 June 2019.

Alternatively, we can calculate the odd days for each month individually:

Total odd days = 6 + 0 + 3 + 2 + 3 + 4 = 18 odd days.

Since 18 is greater than 7, we find the odd days in 18:

$\frac{18}{7} = \frac{2 \times 7 + 4}{7} = 2 \text{ weeks } + 4 \text{ days}$

The remainder is 4. This confirms there are 4 odd days.

Step 3: Determine the Day for 11 June 2019

We know that 11 January 2019 is a Friday and there are 4 odd days between 11 January 2019 and 11 June 2019. We need to add these 4 odd days to Friday.

• Friday + 1 day = Saturday
• Friday + 2 days = Sunday
• Friday + 3 days = Monday
• Friday + 4 days = Tuesday

Therefore, 11 June 2019 will fall on a Tuesday.

Revision Table: Calendar Calculations

Additional Information: Mastering Calendar Problems

Understanding the concept of odd days is fundamental to solving calendar-based day calculation problems quickly. Here are some key points:

• Every 7 days, the day of the week repeats. This is why we care about the remainder when dividing by 7.
• The number of days in each month is crucial: 30 days have 2 odd days ($30 \div 7$, Remainder 2), and 31 days have 3 odd days ($31 \div 7$, Remainder 3). February has 0 odd days in a normal year (28 days) and 1 odd day in a leap year (29 days).
• When calculating odd days over multiple years, remember to account for leap years falling within the period. Each leap year adds an extra odd day (2 instead of 1) compared to a normal year.
• Calculating odd days between two dates within the same year involves summing the days in the intervening months (or parts of months) and finding the total odd days.
• When moving forward in time, add the odd days to the starting day. When moving backward, subtract the odd days.

Practice with different date ranges and leap year scenarios will help you become proficient in solving these types of logical reasoning questions.