In a month of 29 days, the second Thursday falls on the 13th day of the month. What day of the week will be the second last day of the month?
Friday
Solving the 29-Day Month Calendar Puzzle
This problem asks us to determine the day of the week for the second last day of a month that has exactly 29 days, given that the second Thursday of this month falls on the 13th day.
Understanding the Given Information
- The month has 29 days in total.
- The second Thursday of the month is on the 13th.
Finding the Dates of Thursdays
We know that the second Thursday is on the 13th. Days of the week repeat in a 7-day cycle. To find the dates of other Thursdays in the month, we can add or subtract multiples of 7 from the 13th.
- Second Thursday: 13th
- First Thursday: $13 - 7 = 6$. So, the 6th is the first Thursday.
- Third Thursday: $13 + 7 = 20$. So, the 20th is the third Thursday.
- Fourth Thursday: $20 + 7 = 27$. So, the 27th is the fourth Thursday.
Since the month only has 29 days, the Thursdays in this month fall on the 6th, 13th, 20th, and 27th.
Determining the Second Last Day of the Month
The month has 29 days. The last day is the 29th. The second last day is the day before the last day.
Second last day = Total number of days in the month - 1
Second last day = $29 - 1 = 28$th day.
So, we need to find the day of the week for the 28th day of the month.
Calculating the Day for the 28th
We have identified that the 27th of the month is a Thursday. To find the day for the 28th, we just need to consider the day immediately following the 27th.
- If the 27th is Thursday, then the day after, the 28th, must be Friday.
Let's confirm this with the dates around the end of the month:
| Date | Day of the Week |
|---|---|
| 26th | Wednesday |
| 27th | Thursday |
| 28th | Friday |
| 29th | Saturday |
Based on our calculation, the 28th day of the month will be a Friday.
Revision Table: Calendar Day Calculation Concepts
| Concept | Explanation |
|---|---|
| Day Cycle | Days of the week repeat every 7 days (Sunday, Monday, ..., Saturday, Sunday, ...). |
| Finding Same Day | If a specific date has a certain day, the same day will occur 7 days later, 14 days later, 21 days later, and so on (i.e., date $+ 7n$). Similarly, it occurred 7 days earlier, 14 days earlier, etc. (i.e., date $- 7n$). |
| Finding Next Day | If you know the day for date 'X', the day for date 'X+1' is the next day in the weekly cycle. |
| Finding Previous Day | If you know the day for date 'X', the day for date 'X-1' is the previous day in the weekly cycle. |
Additional Information: Calendar Calculations and Variations
Calendar problems often involve understanding the cyclical nature of days and months. Key factors include:
- The number of days in the month (28, 29, 30, or 31). A 29-day month is typically February in a leap year.
- Identifying a known date and its corresponding day of the week.
- Using the 7-day cycle to find other dates with the same day or to find the day for a different date.
- Leap years affect the number of days in February (29 instead of 28) and can shift the day of the week for subsequent dates in the year by one day after February 29th. In this specific problem, the 29-day month is given, so we don't need to determine if it's a leap year February; the length is stated directly.
Calculations like finding the day for date 'Y' when the day for date 'X' is known often involve finding the difference between the dates ($Y - X$) and then finding the remainder when this difference is divided by 7. This remainder tells you how many days forward (or backward, if the difference is negative) from the known day the target day is.
Important Questions from Clock and Calendar
If 19 July 2000 was a Wednesday, then what would be the day of the week on 15 June 2012?
What day of the week was 31 st January 2007?
What was the day of the week on 10 June 2011?
What day of the week was 5 February 2008?
What day of the week was 29 June 2010?
