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Well... let's figure it out.

  1. .
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  8. 1 - 8 Here.
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  18. 2 - 8 Here
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  26. ..
  27. ..
  28. 3 - 8 Here
  29. .
  30. ..
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  33. .
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  38. 4 - 8 Here
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  48. 5 - 8 Here
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  58. 6 - 8 Here
  59. .
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  68. 7 - 8 Here
  69. .
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  77. .
  78. 8 - 8 Here
  79. .
  80. 9 - 8 Here
  81. 10 - 8 Here
  82. 11 - 8 Here
  83. 12 - 8 Here
  84. 13 - 8 Here
  85. 14 - 8 Here
  86. 15 - 8 Here
  87. 16 - 8 Here
  88. 17 & 18 - Two 8's Here
  89. 19 - 8 Here
  90. .
  91. .
  92. .
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  98. 20 - 8 Here
  99. .
  100. So the answer is, between the number 1 and 100 an 8 appears 20 times.

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Q: How many times digit 8 appears from 1 to 100 in detail show?
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