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Math Help - How many patterns?

  1. #1
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    How many patterns?

    Hello.

    Let's say you have a 4x4 grid, you can make patterns by using any number of squares, connected or not. So, one pattern may use just one square, top left, another may use one top right, another may use the entire top row etc. How many patterns can you make from that 4x4 grid?

    Cheers.

    N.
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  2. #2
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    Quote Originally Posted by theNoodler View Post
    Let's say you have a 4x4 grid, you can make patterns by using any number of squares, connected or not. So, one pattern may use just one square, top left, another may use one top right, another may use the entire top row etc. How many patterns can you make from that 4x4 grid?
    There are a great many ways that one could read this question.
    Let's say that we will use only one color, red, and the grid has a fixed orientation.
    There are 16 sub-squares in a 4\times 4 grid.
    So there are 2^{16} subsets of those squares.

    Is that what you are asking?
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  3. #3
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    Hello.

    OK, sorry, I'll try oto be more specific. We are using one colour.

    One pattern could be:

    XOOO
    OOOO
    OOOO
    OOOO

    another could be:

    XXOO
    OOOO
    OOOO
    OOOO

    and yet another could be:

    XOOO
    XOOO
    XOOO
    XOOO

    it's simply that a pattern could use one or all the squares, or any number in between, any orientation. Does that help?

    Thanks.
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  4. #4
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    Look at the graphic.
    If that could one of the patterns, then the answer is still 2^{16}.

    If not, you need to set out the rules.
    Attached Thumbnails Attached Thumbnails How many patterns?-pat-sq.gif  
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  5. #5
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    Hello.

    That is perfect, thank you.
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