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How many number of times will the digit

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Intern
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How many number of times will the digit [#permalink] New post 30 Oct 2003, 05:33
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How many number of times will the digit тАШ7' be written when listing the integers from 1 to 1000?


(1) 271 (2) 300 (3) 252 (4) 304 (5) 312
Manager
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 [#permalink] New post 30 Oct 2003, 06:09
300 times just like any other integer but 0. I'd say 1 also but 1 is dependent on whether the boundaries are inclusive.
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 [#permalink] New post 30 Oct 2003, 06:14
one-position numbers: one 7 = 1
two-position numbers: X7 (eight), 7X (nine), and 77 (two) = 19
three-position numbers: XX7 (8*9), X7X (8*9), 7XX (9*9), 77X (nine*2), 7X7 (nine*2), X77 (eight*2), 777 (three)

1+19+72+72+81+18+18+16+3=300

oops :oops: :oops:

any other approaches?
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 [#permalink] New post 30 Oct 2003, 07:18
stolyar wrote:
one-position numbers: one 7 = 1
two-position numbers: X7 (eight), 7X (nine), and 77 (two) = 19
three-position numbers: XX7 (8*9), X7X (8*9), 7XX (9*9), 77X (nine*2), 7X7 (nine*2), X77 (eight*2), 777 (three)

1+19+72+72+81+18+18+16+3=300

oops :oops: :oops:

any other approaches?

stolyar,

I derived this formula (out of my habit) after some calculations and testing that seems to work well so far.

For this example:
n = # of zero's the higher range ...... (3 in this case)
S = # of times a digit occurs ...... (# of times 7 occurs)

S = n * 10^(n - 1)
= 3 * 10^2
= 300

Let me know if anyone wants the theoretical proof for my formula.
  [#permalink] 30 Oct 2003, 07:18
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