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Math Help - a problem can't understand it

  1. #1
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    a problem can't understand it

    here is the link of the problem but i can't understand the form of numbers
    https://www.spoj.pl/problems/EASYPROB/
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  2. #2
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    Quote Originally Posted by mido22 View Post
    here is the link of the problem but i can't understand the form of numbers
    https://www.spoj.pl/problems/EASYPROB/
    It's a combination of brain teaser and knowing something about binary.

    137 is related to the string "2(2(2)+2+2(0))+2(2+2(0))+2(0)" in that 137=2^{2^2+2^1+2^0}+2^{2^1+2^0}+2^0. The binary representation of 137 is 10001001. See it?
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  3. #3
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    i know about the binary and i understand the

    but what is the relation betn. the binary of 137 and this form
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  4. #4
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    do u meant that in this binary no.

    10001001
    the first term (1000) -> the power will be three terms as zeros 2^2+2^1+2^0

    and second term (100) -> the power will be two terms as zeros 2^1+2^0

    and so on

    but here for example
    73=2(2(2)+2) +2(2+2(0)) +2(0)
    the binary of 73 = 100 100 1
    this binary won't help me as i understand
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  5. #5
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    Quote Originally Posted by mido22 View Post
    i know about the binary and i understand the

    but what is the relation betn. the binary of 137 and this form
    Quote Originally Posted by mido22 View Post
    do u meant that in this binary no.

    10001001
    the first term (1000) -> the power will be three terms as zeros 2^2+2^1+2^0

    and second term (100) -> the power will be two terms as zeros 2^1+2^0

    and so on

    but here for example
    73=2(2(2)+2) +2(2+2(0)) +2(0)
    the binary of 73 = 100 100 1
    this binary won't help me as i understand
    I am a bit free with my notation in order to write compactly, I think it is legible

    73_{10} = 1001001_2 = 2^6 + 2^3 + 2^0 = 2^{110_2} + 2^{11_2} + 2^0 = 2^{2^2+2^1} + 2^{2^1+2^0} + 2^0
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  6. #6
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    Quote Originally Posted by undefined View Post
    I am a bit free with my notation in order to write compactly, I think it is legible

    73_{10} = 1001001_2 = 2^6 + 2^3 + 2^0 = 2^{110_2} + 2^{11_2} + 2^0 = 2^{2^2+2^1} + 2^{2^1+2^0} + 2^0
    i still understanding all except
    how can u get that the power of first term is 6 and second is 3 and third is 0 from the binary
    if i'mnot silly plz till me what usage of binary here
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  7. #7
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    to understand what i want
    i understood the image u put and
    binary of 6 -> 110 and so on for powers

    but how can u get the powers 6,3,0
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  8. #8
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    Quote Originally Posted by mido22 View Post
    i still understanding all except
    how can u get that the power of first term is 6 and second is 3 and third is 0 from the binary
    if i'mnot silly plz till me what usage of binary here
    So in decimal we have for example 12345 = 5\cdot10^0 + 4\cdot10^1 + 3\cdot10^2 + 2\cdot10^3 + 1\cdot10^4. More symbolically, write an n-digit decimal number as a_{n-1}a_{n-2}\dots a_1a_0, then it is equal to \displaystyle \sum_{k=0}^{n-1} a_k\cdot10^k.

    It is the same in binary, just replace the 10 with 2.
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  9. #9
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    i begin to understand u thx very much
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  10. #10
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    Quote Originally Posted by mido22 View Post
    to understand what i want
    i understood the image u put and
    binary of 6 -> 110 and so on for powers

    but how can u get the powers 6,3,0
    Quote Originally Posted by mido22 View Post
    i begin to understand u thx very much
    If it's still not clear, see attached image
    Attached Thumbnails Attached Thumbnails a problem can't understand it-binary_convert.png  
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  11. #11
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    Quote Originally Posted by undefined View Post
    If it's still not clear, see attached image
    nw it is very very clear thx very much
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