0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99,
101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222,
232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353,
363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484,
494, 505, 515, 525, 535, 545, 555, 565, 575, 585, 595, 606, 616,
626, 636, 646, 656, 666, 676, 686, 696, 707, 717, 727, 737, 747,
757, 767, 777, 787, 797, 808, 818, 828, 838, 848, 858, 868, 878,
888, 898, 909, 919, 929, 939, 949, 959, 969, 979, 989, 999
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1097
A palindromic number is a number that remains the same when its digits are reversed. Between 1000 and 2000, the possible palindromic numbers have the form "ABBA" where A and B are digits from 1 to 9. There are 9 options for A (1-9) and 10 options for B (0-9), but we exclude the case where A is 0. Therefore, there are 9 * 10 = 90 palindromic numbers between 1000 and 2000.
If you think about the digits, you can rewrite them as ABBA, with A being one digit and B being another: A can be 1-9 and B can be 0-9. Since A has to be 1, B can be 0-9, leaving 10 palindromic numbers.
To find the number of palindromic numbers between 1000 and 10000, we need to consider that a palindrome is a number that reads the same forwards and backwards. For a four-digit number to be palindromic, the first and last digits must be the same, and the middle two digits must be the same. Therefore, the total number of palindromic numbers between 1000 and 10000 is determined by the number of options for the first two digits (10 options, 1-9 excluding 0) and the last two digits (10 options as well). This gives us a total of 10 * 10 = 100 palindromic numbers between 1000 and 10000.
1000