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# How many number of times will the digit

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Intern
Joined: 10 Oct 2003
Posts: 45
Location: Finland
Followers: 1

Kudos [?]: 0 [0], given: 0

How many number of times will the digit [#permalink]  30 Oct 2003, 05:33
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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
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
Joined: 26 Aug 2003
Posts: 233
Location: United States
Followers: 1

Kudos [?]: 2 [0], given: 0

300 times just like any other integer but 0. I'd say 1 also but 1 is dependent on whether the boundaries are inclusive.
SVP
Joined: 03 Feb 2003
Posts: 1608
Followers: 6

Kudos [?]: 76 [0], given: 0

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

any other approaches?
Manager
Joined: 26 Aug 2003
Posts: 233
Location: United States
Followers: 1

Kudos [?]: 2 [0], given: 0

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

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.
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