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Math Help - How many triangles?

  1. #1
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    How many triangles?

    Hi,

    How many triangles are in this picture:

    How many triangles?-161920_168316136537227_5561635_s.jpg

    Kind regards,

    Kepler
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by kepler View Post
    Hi,

    How many triangles are in this picture:

    <image>

    Kind regards,

    Kepler
    Nice problem. I might have counted wrong.

    Spoiler:

    There are 9 vertices/points of intersection, and consider sets of three of them. We have 3+1+2+2*C(4,3) = 14 sets that are collinear, where C(n,k) is binomial coefficient. Then consider sets of two of them. I count 6 that are not connected. Each of these 6 would have given 7 triangles, had they been connected. So I get C(9,3) - 14 - 6*7 = 28 total.
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  3. #3
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    Hi,

    yep, that's my guess too.

    Kind regards,

    Kepler
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  4. #4
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    Quote Originally Posted by kepler View Post
    Hi,

    How many triangles are in this picture:

    Click image for larger version. 

Name:	161920_168316136537227_5561635_s.jpg 
Views:	331 
Size:	6.3 KB 
ID:	20537

    Kind regards,

    Kepler
    Counting sequentially......

    If there are no internal lines, 1 triangle.
    Draw the vertical line, 2 new triangles.
    Draw the line from the left vertex to the right side, 5 new triangles.
    Draw the line from the right vertex to the left side, 6 new triangles.
    Draw the line from the left side to the mid-base, 7 new triangles.
    Draw the line from the right side to the mid-base, 7 new triangles.

    Total 28.
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  5. #5
    Newbie beeliz's Avatar
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    I found 34 triangles
    picture of them: How many triangles?-triangles.jpg
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  6. #6
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    Well done!

    I miscounted.
    My totals should have been....

    No internal lines.....1 triangle
    1 internal line........2 more
    3 lines..................5 more
    4 lines..................8 more
    5 lines..................8 more
    6 lines..................10 more
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  7. #7
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    Quote Originally Posted by beeliz View Post
    I found 34 triangles
    picture of them: Click image for larger version. 

Name:	triangles.jpg 
Views:	120 
Size:	593.9 KB 
ID:	20770
    33 and 34 are duplicating your 4 and 5.

    I agree with the total, though...
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  8. #8
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    Here's another counting process
    Attached Thumbnails Attached Thumbnails How many triangles?-triangles.jpg  
    Last edited by Archie Meade; February 13th 2011 at 09:43 AM.
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  9. #9
    Newbie beeliz's Avatar
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    Quote Originally Posted by tom@ballooncalculus View Post
    33 and 34 are duplicating your 4 and 5.

    I agree with the total, though...
    whoooops. well I found 34 somewhere...

    oh in the image Archie Meade posted, it's #2 in the fourth triangle and #1 in the sixth triangle that I missed in my picture. but I found them the first time I counted during a boring english class


    better picture: How many triangles?-tiangles-33-34.jpg because I'm a perfectionist
    Last edited by beeliz; February 13th 2011 at 01:37 PM. Reason: added picture
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