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One writes a list of numbers from 0 to 10000. How many

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One writes a list of numbers from 0 to 10000. How many [#permalink] New post 26 Sep 2003, 10:33
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One writes a list of numbers from 0 to 10000. How many zeroes will he have to write?
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Joined: 07 Jul 2003
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 [#permalink] New post 26 Sep 2003, 20:09
Quick in the head guess:

1000 + 1000 + 1000 + 1000 - 9 - 99 - 999 + 1 =

1000 + 991 + 901 + 1 + 1 = 2894
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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 [#permalink] New post 26 Sep 2003, 22:58
cool and amazing, my approach is longer

consider one-digit numbers: the only zero is there, 1.
consider two-digit numbers: a zero cannot be on the first place; it can be only on the second; thus, 9*1=9
consider three-digit numbers: with one zero--2*9*9; with two zeroes--9*2=18, total--180
consider four-digit numbers: with one zero--3*9*9*9; with two zeroes-- 3*9*9*2; with three zeroes--9*3; total-- 2700
consider 10000: 4 zeroes

Overall: 1+9+180+2700+4=2894

Please, elaborate your approach.
  [#permalink] 26 Sep 2003, 22:58
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One writes a list of numbers from 0 to 10000. How many

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