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experimentX

how many triangles do you see in figure.

  • 2 years ago
  • 2 years ago

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

    • 2 years ago
  3. experimentX
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    overlapping

    • 2 years ago
  4. myko
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    39?

    • 2 years ago
  5. King
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    43 or 45

    • 2 years ago
  6. King
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    43-45

    • 2 years ago
  7. King
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    44 i think

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

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

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

    • 2 years ago
  11. King
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    45 is the answer

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

    • 2 years ago
  13. experimentX
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    i think 46

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

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

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

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

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

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

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

    • 2 years ago
  21. Diyadiya
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    I got 46

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

    • 2 years ago
  23. King
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    hw diya?

    • 2 years ago
  24. Diyadiya
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    Wait letme count again

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

    • 2 years ago
  26. King
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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!!

    • 2 years ago
  27. experimentX
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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?

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

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

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

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

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

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

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

    • 2 years ago
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  35. experimentX
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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.

    • 2 years ago
  36. philips13
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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

    • 2 years ago
  37. TuringTest
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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?

    • 2 years ago
  38. TuringTest
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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?

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

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

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

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

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

    • 2 years ago
  44. TuringTest
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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

    • 2 years ago
  45. FoolForMath
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    :)

    • 2 years ago
  46. Callisto
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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

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

    • 2 years ago
  48. kr7210
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    48 i guess

    • one year ago
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