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experimentX

  • 4 years ago

how many triangles do you see in figure.

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  1. experimentX
    • 4 years ago
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  2. myko
    • 4 years ago
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    overlapping or no?

  3. experimentX
    • 4 years ago
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    overlapping

  4. myko
    • 4 years ago
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    39?

  5. King
    • 4 years ago
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    43 or 45

  6. King
    • 4 years ago
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    43-45

  7. King
    • 4 years ago
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    44 i think

  8. experimentX
    • 4 years ago
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    let's see, we have 1 huge triangle

  9. experimentX
    • 4 years ago
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    the no of smallest triangle is 9+7+5+3+1 = 26

  10. experimentX
    • 4 years ago
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    a little bigger triangle .. we have 13, so total is 40 until now

  11. King
    • 4 years ago
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    45 is the answer

  12. experimentX
    • 4 years ago
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    no .. but quite close

  13. experimentX
    • 4 years ago
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    i think 46

  14. experimentX
    • 4 years ago
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    Oo... sorry @King 's right i made mistake in above summation

  15. experimentX
    • 4 years ago
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    can you explain your approach?

  16. King
    • 4 years ago
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    so 45 is rite?

  17. experimentX
    • 4 years ago
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    9+7+5+3+1 = 26 .. from this i was able to deduce 46

  18. King
    • 4 years ago
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    nos.of small triangles=25 not 26!!@experimentX

  19. King
    • 4 years ago
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    9+7=16 5+3+1=9 16+9=25!!

  20. experimentX
    • 4 years ago
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    still i cannot come up with general formula ...!

  21. Diyadiya
    • 4 years ago
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    I got 46

  22. King
    • 4 years ago
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    no.of triangles=level of @experimentX

  23. King
    • 4 years ago
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    hw diya?

  24. Diyadiya
    • 4 years ago
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    Wait letme count again

  25. experimentX
    • 4 years ago
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    lol ... quite a matching no.

  26. King
    • 4 years ago
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    no.of small triangles=25 no.of triangles with 2 rows of small triangles=10 no.of triangles with 3 rows of small triangles=6 no.of triangles with 4 rows of small triangles=3 1 big full triangle so, 25+10+6+3+1 =45!!

  27. experimentX
    • 4 years ago
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    no.of triangles with 2 rows of small triangles=10 ...it think this should be 13, aren't we missing inverted triangles?

  28. .Sam.
    • 4 years ago
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    If overlapping I found 45

  29. King
    • 4 years ago
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    yeah!!sry so its 48

  30. Callisto
    • 4 years ago
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    not include the inverted ones :(

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  31. King
    • 4 years ago
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    there are no inverted ones wid 3 or 4 rows so it has to be 48...i think

  32. King
    • 4 years ago
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    so answer is 48!!

  33. King
    • 4 years ago
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    @experimentX u der?if u are happy and satisfied wid answer close the question....

  34. experimentX
    • 4 years ago
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    i guess 48 is the right answer ...

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  35. experimentX
    • 4 years ago
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    still i was looking some sorts of permutations and combinations to this get this answer ... anyway thanks to all who tried.

  36. philips13
    • 4 years ago
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    floor(n(n+2)(2n+1)/8) where n is the number of triangles on a side in your specific case, n=5

  37. TuringTest
    • 4 years ago
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    if this problem is only about the dark triangles it is kind of boring... isn't it about using the inverted ones as well as callisto suggested?

  38. TuringTest
    • 4 years ago
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    actually, I'm seeing more problems with the solution here isn't there much more going on that we are ignoring?

  39. FoolForMath
    • 4 years ago
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    @philips13 Gave the right answer. \[\huge \lfloor \normalsize \frac{ (n(n+2)(2n+1)}8 \huge \rfloor \]

  40. TuringTest
    • 4 years ago
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    Oh yeah? Ok thanks, but now I wanna decipher it you seem to be familiar with this theorem FFM :P

  41. FoolForMath
    • 4 years ago
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    I am familiar with almost everything labelled interesting :P http://www.mathematik.uni-bielefeld.de/~sillke/SEQUENCES/grid-triangles

  42. TuringTest
    • 4 years ago
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    You think we haven't noticed? Where do you get this encyclopedic knowledge?!

  43. FoolForMath
    • 4 years ago
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    Lol, I was kidding. I am just an ordinary guy with some practice :)

  44. TuringTest
    • 4 years ago
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    yeah, whatever... :P I'm not sure I understand some of the notation on the link you gave me, but I'm sure I'll get it after hacking away at it for a while. Thanks :D

  45. FoolForMath
    • 4 years ago
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    :)

  46. Callisto
    • 4 years ago
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    I was thinking why i couldn't get the answer 48 when i did the calculation. But then from the website, it says that number of triangle = n*(n+2)*(2n+1)/8 for n even = (n*(n+2)*(2n+1) - 1)/8 for n odd So, I got 48 finally... BTW, it's experimentX who first suggested that we were missing the inverted triangles

  47. experimentX
    • 4 years ago
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    thanks to all for reply!! and finally it's complete!

  48. kr7210
    • 3 years ago
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    48 i guess

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