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Find the total number of four-digit palindromes. (Recall that a palindrome is a non-negative sequence of digits which reads the same forwards and backwards, such as 1331. Zero cannot be the first digit.)

Apr 30, 2018

#1
+22290
+2

Find the total number of four-digit palindromes.

(Recall that a palindrome is a non-negative sequence of digits which reads the same forwards and backwards, such as 1331. Zero cannot be the first digit.)

There are 90 four-digit palindromes.

$$\begin{array}{|r|r|r|} \hline & n & \text{palindrome } a(n) \\ \hline 1. & 110& 10\ 01 \\ 2. & 111& 11\ 11 \\ 3. & 112& 12\ 21 \\ 4. & 113& 13\ 31 \\ 5. & 114& 14\ 41 \\ 6. & 115& 15\ 51 \\ 7. & 116& 16\ 61 \\ 8. & 117& 17\ 71 \\ 9. & 118& 18\ 81 \\ 10. & 119& 19\ 91 \\ \hline 11. & 120& 20\ 02 \\ 12. & 121& 21\ 12 \\ 13. & 122& 22\ 22 \\ 14. & 123& 23\ 32 \\ 15. & 124& 24\ 42 \\ 16. & 125& 25\ 52 \\ 17. & 126& 26\ 62 \\ 18. & 127& 27\ 72 \\ 19. & 128& 28\ 82 \\ 20. & 129& 29\ 92 \\ \hline 21. & 130& 30\ 03 \\ 22. & 131& 31\ 13 \\ 23. & 132& 32\ 23 \\ 24. & 133& 33\ 33 \\ 25. & 134& 34\ 43 \\ 26. & 135& 35\ 53 \\ 27. & 136& 36\ 63 \\ 28. & 137 & 37\ 73 \\ 29. & 138& 38\ 83 \\ 30. & 139& 39\ 93 \\ \hline 31. & 140& 40\ 04 \\ 32. & 141& 41\ 14 \\ 33. & 142& 42\ 24 \\ 34. & 143& 43\ 34 \\ 35. & 144& 44\ 44 \\ 36. & 145& 45\ 54 \\ 37. & 146& 46\ 64 \\ 38. & 147& 47\ 74 \\ 39. & 148& 48\ 84 \\ 40. & 149& 49\ 94 \\ \hline 41. & 150& 50\ 05 \\ 42. & 151& 51\ 15 \\ 43.& 152& 52\ 25 \\ 44. & 153& 53\ 35 \\ 45. & 154& 54\ 45 \\ 46. & 155& 55\ 55 \\ 47. & 156& 56\ 65 \\ 48. & 157& 57\ 75 \\ 49. & 158& 58\ 85 \\ 50. & 159& 59\ 95 \\ \hline 51. & 160& 60\ 06 \\ 52. & 161& 61\ 16 \\ 53. & 162& 62\ 26 \\ 54. & 163& 63\ 36 \\ 55. & 164& 64\ 46 \\ 56. & 165& 65\ 56 \\ 57. & 166& 66\ 66 \\ 58. & 167& 67\ 76 \\ 59. & 168& 68\ 86 \\ 60. & 169& 69\ 96 \\ \hline 61. & 170& 70\ 07 \\ 62. & 171& 71\ 17 \\ 63. & 172& 72\ 27 \\ 64. & 173& 73\ 37 \\ 65. & 174& 74\ 47 \\ 66. & 175& 75\ 57 \\ 67. & 176& 76\ 67 \\ 68. & 177& 77\ 77 \\ 69. & 178& 78\ 87 \\ 70. & 179& 79\ 97 \\ \hline 71. & 180& 80\ 08 \\ 72. & 181& 81\ 18 \\ 73. & 182& 82\ 28 \\ 74. & 183& 83\ 38 \\ 75. & 184& 84\ 48 \\ 76. & 185& 85\ 58 \\ 77. & 186& 86\ 68 \\ 78. & 187& 87\ 78 \\ 79. & 188& 88\ 88 \\ 80. & 189& 89\ 98 \\ \hline 81. & 190& 90\ 09 \\ 82. & 191& 91\ 19 \\ 83. & 192& 92\ 29 \\ 84. & 193& 93\ 39 \\ 85. & 194& 94\ 49 \\ 86. & 195& 95\ 59 \\ 87. & 196& 96\ 69 \\ 88. & 197& 97\ 79 \\ 89. & 198& 98\ 89 \\ 90. & 199& 99\ 99 \\ \hline \end{array}$$

Apr 30, 2018
#2
+101151
+1

Here's another way

We have 9 ways to select the first digit  and 10  ways to select the second digit

So.....the number of 4 digit palindromes is  just

9 * 10   =

90

Apr 30, 2018