Palindrome Pattern

From 11 to 99 we have 9 .. From 101 to 191we have 10 palindromes So the number of palindromes from 11 to 1000 should equal 9 * 10 + 9 = 99 palindromes .. ......... From 1001 to 1991 we have 10 palindromes .. So from 1000 to 10000 we have 9 * 10 =90 palindromes .. The number of palindromes from 11 to 10000 = 99 + 90 =189 .. This is a simple solution ..

We examine palindromes by number of digits.

For a 2-digit palindrome, there are 9 choices choices for the first digit(no zero!). The second digit must be the same, so there are 9 total.

For a 3-digit palindrome, there are 9 choices choices for the first digit and 10 choices for the second digit(including 0). The third digit must be the same as the first digit, so there are 9x10 = 90 palindromes.

For a 4-digit palindrome, There are 9 choices for the first digit and 10 choices for the second digit. The first digit is the same as the fourth digit, and the second is the same as the third, so there are 9x10 = 90 palindromes.

Therefore, the total number of palindromes between 10 and 10000 is 9 + 90 + 90 = 189.

1 digit: 9 (1,2,...,9) 2 digit: 9 (11,22,...,99) 3 digit: 9∗10 ( 0 , 1 , 2 ,..., 9 ; 9 possibilities for each ) 4 digit: 9∗10 ( 00 , 11 , 22 ,..., 99*; 9 possibilities for each *) Total palindromes: =9+90+90 =189