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Math Help - Bases?!?!

  1. #1
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    Bases?!?!

    Find the missing numbers in the following sequence:
    10,11,12,13,14,15,16,17,20,22,24,31,100,____,____

    I don't know where to start. I know that we have been working with different bases in my math class but I can't think of where to start. Can you explain to me how this works?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by t-lee View Post
    Find the missing numbers in the following sequence:
    10,11,12,13,14,15,16,17,20,22,24,31,100,____,____

    I don't know where to start. I know that we have been working with different bases in my math class but I can't think of where to start. Can you explain to me how this works?
    What does this have to do with bases?

    -Dan
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  3. #3
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    Hello, t-lee!

    This is a classic (old) problem . . .


    Find the missing numbers in the following sequence:
    10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, 31, 100, __, __

    The next two numbers are: 121 and 10000.

    The number "sixteen" is written in base 16, 15, 14, 13, 12, ... , 4, 3, 2.


    Check it out . . .

    \begin{array}{cccccccc}16 = 10_{16}\\ 16 = 11_{15} \\ 16 = 12_{13} \\  \vdots \\ 16 = 31_5 \\ 16 = 100_4 \\ 16 = 121_3 \\ 16 = 10000_2\end{array}

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    Quote Originally Posted by Soroban View Post

    This is a classic (old) problem . . . [/size]
    How many "classic riddles" do you know. It seems anyone asks a question you have an answer in the response of a "classic riddle". It is horrific.
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, t-lee!

    This is a classic (old) problem . . .



    The next two numbers are: 121 and 10000.

    The number "sixteen" is written in base 16, 15, 14, 13, 12, ... , 4, 3, 2.


    Check it out . . .

    \begin{array}{cccccccc}16 = 10_{16}\\ 16 = 11_{15} \\ 16 = 12_{13} \\ \vdots \\ 16 = 31_5 \\ 16 = 100_4 \\ 16 = 121_3 \\ 16 = 10000_2\end{array}

    Hah! I love it!!

    -Dan
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