No.
1001,1111,1221,1331,1441,1551,1661,1771,1881,1991,2002,2112,2222,2332,2442,2552,2662,2772,2882,2992,3003,3113,3223,3333,3443,3553,3663,3773,3883,3993,4004,4114,4224,4334,4444,4554,4664,4774,4884,4994: 40 numbers in all.
40 palindromes.
40. Excluding numbers starting with 0.
There are not just 13 non-palindromic numbers. Most numbers are non-palindromic.
Whole number palindromes between 10 and 40 are: 11, 22, 33 There are, in theory, an infinite number of palindromic decimal numbers in between - but just three palindromic integers.
There are 90 palindromic numbers between 100 and 1000
The sum of two palindromic numbers is not necessarily a palindromic number. For example, adding the palindromic numbers 121 and 131 gives 252, which is also a palindrome. However, adding 121 and 122 results in 243, which is not a palindrome. Therefore, while some sums of palindromic numbers can be palindromic, it is not a guaranteed outcome.
31 and 37
No.
Nobody went out to create them: some numbers simply happen to be palindromic and others don't.
Palindromic numbers occur with varying frequency depending on the range considered. In any given set of numbers, the likelihood of encountering a palindromic number increases as the range expands. For example, among one-digit numbers, all are palindromic, while in larger ranges, the density decreases but still remains significant. Overall, palindromic numbers are not rare and can be found throughout the number system.
infinite