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How many 0's are there in the numbers 1-2001?

 

Thank you!

 Oct 20, 2019
 #1
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+1

There are 494 zeros between 1 and  2001.

 Oct 20, 2019
 #2
avatar+108675 
+1

From 1 to 9        none

From 10 to 99  there are  9

Now I will look at numbers from 100 to 999 =

  zero in the middle but not at end = 9*1*9 = 81

  zero at the end but not in middle = 9*9*1 = 81

  zero in middle and at end = 9*1*1=9 numbers  that is 18 zeros

Total for 2 digit numbers = 9+81+81+18 = 189

 

Now look at numbers 1000 to 1999

  2 zeros = 1*9*3C2 = 9*3 = 27numbers = 54 zeros

   3 zeros = 1number = 3 zeros

  1 zero = 1*9*9 = 81 zeros   Edit:  I forgot to times this by 3      243

2000 has 3 zeros

Total for 3 digit numbers is   54+3+243+3 = 303


Grand total appears to be   189+303 = 492     (I did not include 2001)

 

Thanks Guest :)

 Oct 20, 2019
edited by Melody  Oct 20, 2019
 #3
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+1

From 1 to 9 =None
From 10 to 99 = 9
From 100 to 199 =20
From 200 to 999 =160
From 1000 to 1999 =300
From 2000 to 2001(inclusive) =5
Grand Total = 9 + 20 + 160 + 300 + 5 =494 zeros

P.S. If you don't want 2001 included, then:494 - 2 =492 zeros.

 Oct 20, 2019
edited by Guest  Oct 20, 2019
 #4
avatar+108675 
+1

The only part where our answers differ ( i think) is that 

from 1000 to 1999   

     you got 300

        I got   141

 

 

I will check what i did

    3 zero numbers is just 1000 so that is 3 zeros

     2 zero numbers  the none zero can be in the 2nd 3rd or 4th place that is 3 permutations

      so there will be    100*    = 1*1*1*9  *3   =  27numbers   =  54 zeros

    1 zero numbers  

           1**0   the zero can be in 3 places so

           there will be 1*9*9*1*3 = 243 numbers totalling 243 zeros

 

so that is    3+54+243 = 300

 

Just like guest  said - so now we are in agreement   laugh

Melody  Oct 20, 2019

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