Some poeple believe that Jan 1,2000is the first day of the 21st century.Other poeple beleive that the honor belongs to the Jan 1,2001.But everyone should agree that Jan 1,2002 is the first"sum-day" of the new century when you write out that date in standard notation,it becomes 01/01/02,and 1+1=2 .More generally,a sum-day is a date in which the day and month add up to the year. With that in mind:What is the last sum-day of the 21st century ?.How many sum-days are there in the 21st century?
The last sum day will be 12/31/43
In 2011 itself, we have:
01/10
02/09
03/08
04/07
05/06
06/05
07/04
08/03
09/02
10/01
To find the last sum-day of the 21st century, we need to determine the highest possible date where the day and month add up to the year. Since the sum-day format is Day/Month/Year, the year should be represented as two digits. Considering this, let's go step by step to find the answer.
1. Determine the highest possible year: The 21st century started on January 1, 2001, and will end on December 31, 2100. So, the last possible year in the 21st century is 2100.
2. Find the highest possible day and month: Since the year is represented as two digits, the highest possible day is 12 (since the highest value for a day is 31). The highest possible month is 12 (since the highest value for a month is also 12).
3. Calculate the sum: If we add the highest day (12) and the highest month (12), we get 24. So, the last sum-day of the 21st century would be December 12, 24 (12/12/24).
Now, let's determine the number of sum-days in the 21st century.
1. Calculate the number of years in the 21st century: The 21st century spans from 2001 to 2100, including both years. So, the total number of years is 2100 - 2001 = 99 years.
2. Determine the possible range for days and months: The range for days is 1 to 31 (since the day of a month can be any value from 1 to 31). The range for months is 1 to 12.
3. Calculate the number of sum-days: For each year, we calculate the number of possible sum-days by checking each day (1 to 31) and each month (1 to 12). If the sum of the day and month equals the two-digit year, we count it as a sum-day.
- For example, for the year 2001, there is no sum-day since no combination of day and month adds up to 01.
- However, for the year 2002, January 2nd (02) is a sum-day.
- We repeat this process for all the years from 2001 to 2100 and count the number of sum-days.
Performing this calculation can be time-consuming. Alternatively, you can write a computer program to automate the process and get the exact count.
So, to summarize:
- The last sum-day of the 21st century is December 12, 24 (12/12/24).
- The number of sum-days in the 21st century needs to be calculated by checking each day and month combination for each year. Alternatively, a computer program can be used to obtain the accurate count.