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

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Joined: 03 Feb 2003
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One writes a list of numbers from 0 to 10000. How many [#permalink]  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?
GMAT Instructor
Joined: 07 Jul 2003
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Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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[#permalink]  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

SVP
Joined: 03 Feb 2003
Posts: 1609
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Kudos [?]: 75 [0], given: 0

[#permalink]  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

[#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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