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Math Help - Of Squares & Cubes

  1. #1
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    Of Squares & Cubes

    The question is...

    The number of integers between 1 & 1000(both inclusive) which are neither perfect squares nor perfect cubes is?

    I sarted off like this-
    (tried to count the number of digits which are perfect squares & cubes)

    1-1-1
    2-4-8
    3-9-27
    4-16-64
    5-25-125
    6-36-216
    7-49-343
    8-64-512
    9-81-729
    10-100-1000
    11-121
    12-144
    .......
    which goes upto 31 squared as 32 square > 1000

    on counting all the red ones i get 40,

    so the answer i got was 960 (which is two less than the given answer)




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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by adhyeta View Post
    The question is...

    The number of integers between 1 & 1000(both inclusive) which are neither perfect squares nor perfect cubes is?

    I sarted off like this-
    (tried to count the number of digits which are perfect squares & cubes)

    1-1-1
    2-4-8
    3-9-27
    4-16-64
    5-25-125
    6-36-216
    7-49-343
    8-64-512
    9-81-729
    10-100-1000
    11-121
    12-144
    .......
    which goes upto 31 squared as 32 square > 1000

    on counting all the red ones i get 40,

    so the answer i got was 960 (which is two less than the given answer)





    You have double counted two elements one of them is

    64=8^2=4^3

    I don't know the other of the top of my head
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    You have double counted two elements one of them is

    64=8^2=4^3

    I don't know the other of the top of my head
    yes another one to go.............

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  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by adhyeta View Post
    yes another one to go.............


    The other is 729=27^2=9^3
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  5. #5
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    Quote Originally Posted by TheEmptySet View Post
    The other is 729=27^2=9^3
    dude! thanks!

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  6. #6
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    your sig is beautiful!
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