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# One writes a list of numbers from 1 to 1000. How many ones

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SVP
Joined: 03 Feb 2003
Posts: 1607
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One writes a list of numbers from 1 to 1000. How many ones [#permalink]  26 Sep 2003, 11:05
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One writes a list of numbers from 1 to 1000. How many ones will he have to write?
SVP
Joined: 03 Feb 2003
Posts: 1607
Followers: 7

Kudos [?]: 87 [0], given: 0

guys, what are you waiting for? give it a try.
Manager
Joined: 13 Aug 2003
Posts: 68
Location: India
Followers: 1

Kudos [?]: 1 [0], given: 0

a tricky one... just giving a shot though... hundrets place 100 + tens place 90 and units 90 == 280.. not too sure still...
Manager
Joined: 13 Aug 2003
Posts: 68
Location: India
Followers: 1

Kudos [?]: 1 [0], given: 0

a tricky one... just giving a shot though... hundrets place 100 + tens place 90 and units 90 == 280.. not too sure still...
Manager
Joined: 26 Aug 2003
Posts: 233
Location: United States
Followers: 1

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

I have this formula I ended up deriving after encountering couple of problems like this one, here it goes:

Setp 1: Make places for as many number of digits as the number of zero's after 1.
Setp 2: The first digit is the number of zeros after 1.
Setp 3: Then rest of the digits are zero.
Setp 4: Add one to this number if your upper range number is included in the count.

So... for this problem

Step 1: _ _ _
Step 2: 3 _ _
Setp 3: 3 0 0
Setp 4: 3 0 1

So total number of zero's between 1 and 1000, inclusive, is 301.

This count formula also works for all other digits except you don't do the Step #4. Of course, this formula has certain rules if your range doesn't end at a number that has 1 and tailing zeros. Which I'll mention some other time when I have more time at hand.

----------

Another way.

(# of zeros) * (Upper Range/10) [+ 1] = total number of 1's in the range
where [+ 1] is optional depending on your upper limit.

In this case:
3 * (1000/10) + 1 = 301
SVP
Joined: 03 Feb 2003
Posts: 1607
Followers: 7

Kudos [?]: 87 [0], given: 0

consider one-digit numbers: the only 1

consider two-digit numbers: X1 (eight such numbers), 1X (nine) and 11. In total there are 8+9+2=19

consider three-digit numbers: XX1 (8*9=72), X1X (8*9=72), 1XX (9*9=81), 11X (9*2=18), 1X1 (9*2=18), X11 (8*2=16), and 111 (3). Total:72+72+81+18+18+16+3=280

1000 gives one 1.

Overall: 1+19+280+1=301
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