If you realize that a 4 digit palindrome is basically a two digit number followed by it's own reverse, you can re-phrase this question as 'how many two digit numbers are there?' Which would then mean that (if you're considering zeros as digits without a non-zero leading term) there would be a 4 digit palindrome 0000 for the two digit 00; a four digit 0110 for the two digit 01; 0220, 02; etc etc. So the number of four digit palindromes would be the same as the quantity of whole numbers from 00 to 99. So I believe the total answer to your question would be 100.
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