Palindromic Number

1. For counting two digit number, like $\overline{ab}$ , it must be $a=b$ . So we get $9$ palindromic number.

$11,22,33,44,55,66,77,88,99$

1. For counting three digit number like $\overline{abc}$ , it must be $a$ and $c$ same and $b$ can be any digit. We choose $a$ in $9$ ways and can choose $b$ in 10 ways. So three digit number can be formed in $9\times10=90$ ways.

$101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353\\ 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515, 525, 535, 545, 555, 565, 575, 585, 595, 606, 616\\ 626, 636, 646, 656, 666, 676, 686, 696, 707, 717, 727, 737, 747, 757, 767, 777, 787, 797, 808, 818, 828, 838, 848, 858, 868, 878\\ 888, 898, 909, 919, 929, 939, 949, 959, 969, 979, 989, 999$

3.For counting four digit number like $\overline{abcd}$ , it must be $a=d$ and $b=c$ . So we can choose $a$ in $9$ ways and can choose $b$ in $10$ ways. So four digit number can be formed in $9\times10=90$ ways.

$1001, 1111, 1221, 1331, 1441, 1551, 1661, 1771, 1881, 1991, 2002, 2112, 2222, 2332, 2442, 2552, 2662, 2772, 2882, 2992, 3003\\ 3113, 3223, 3333, 3443, 3553, 3663, 3773, 3883, 3993, 4004, 4114, 4224, 4334, 4444, 4554, 4664, 4774, 4884, 4994, 5005, 5115\\ 5225, 5335, 5445, 5555, 5665, 5775, 5885, 5995, 6006, 6116, 6226, 6336, 6446, 6556, 6666, 6776, 6886, 6996, 7007, 7117, 7227\\ 7337, 7447, 7557, 7667, 7777, 7887, 7997, 8008, 8118, 8228, 8338, 8448, 8558, 8668, 8778, 8888, 8998, 9009, 9119, 9229, 9339\\ 9449 9559, 9669, 9779, 9889, 9999$

So total $9+90+90=\boxed{189}$