The year 1991 was the last year of the twentieth century whose number is a palindrome,that is,reads the same backward and forward. How many years between the years 2000 and 3000 will be palindromic?

2002

Only one year

10

2002, 2112, 2222,2332,2442,2552,2662,2772,2882,2992

To determine how many years between the years 2000 and 3000 will be palindromic, we can break down the problem into smaller components and analyze it step by step:

Step 1: Analyze the range
Find the total number of years between 2000 and 3000, including both endpoints:
Total number of years = 3000 - 2000 + 1 = 1001 years

Step 2: Determine requirements for a palindromic year
A palindromic year is one that reads the same backward and forward. In this context, it means the year has a four-digit format, and the 1st and 4th digits are the same, while the 2nd and 3rd digits are the same.

Step 3: Determine the possibilities for the 1st and 4th digits
Since the 1st and 4th digits must be the same, we need to determine how many possibilities exist for these digits. Since the range is between 2000 and 3000, the possibilities for the 1st and 4th digits can be any number from 2 to 3.

Step 4: Determine the possibilities for the 2nd and 3rd digits
Since the 2nd and 3rd digits must be the same, we need to determine how many possibilities exist for these digits. Any number from 0 to 9 can be chosen for the 2nd and 3rd digits.

Step 5: Calculate the total possibilities
Multiply the number of possibilities for the 1st and 4th digits by the number of possibilities for the 2nd and 3rd digits:
Total possibilities = (number of possibilities for 1st and 4th digits) x (number of possibilities for 2nd and 3rd digits)

In this case, the number of possibilities for the 1st and 4th digits is 3 (2, 3), and the number of possibilities for the 2nd and 3rd digits is 10 (0-9):
Total possibilities = 3 x 10 = 30

Therefore, there will be a total of 30 palindromic years between 2000 and 3000.