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The written number one occurs only once by itself, or 31 times including where it is part of other numbers. The numeral 1 would appear 53 times.

There are nine units of ten 1-90 but one (eleven) does not include one.

There are twenty-one numbers from 100 to 120 that include one and it occurs twice in the number 101 for a total of 1 + 8 + 22 = 31

Written:

  1. one
  2. twenty-one
  3. thirty-one
  4. forty-one
  5. fifty-one
  6. sixty-one
  7. seventy-one
  8. eighty-one
  9. ninety-one
  10. one hundred
  11. one hundred
  12. and one
  13. one hundred and two
  14. one hundred and three
  15. one hundred and four
  16. one hundred and five
  17. one hundred and six
  18. one hundred and seven
  19. one hundred and eight
  20. one hundred and nine
  21. one hundred and ten
  22. one hundred and eleven
  23. one hundred and twelve
  24. one hundred and thirteen
  25. one hundred and fourteen
  26. one hundred and fifteen
  27. one hundred and sixteen
  28. one hundred and seventeen
  29. one hundred and eighteen
  30. one hundred and nineteen
  31. one hundred and twenty

Numerals:

1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, [twelve times]

21, 31, 41, 51, 61, 71, 81, 91 [eight times]

100, 101, 102, 103, 104, 105, 106, 107, 108, 109 [eleven times]

110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120 [ twenty-two times]

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Q: How many time does the number one occur between one and one hundred and twenty inclusive?
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