how many triangles do you see in figure.

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how many triangles do you see in figure.

Mathematics
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overlapping or no?
overlapping

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Other answers:

39?
43 or 45
43-45
44 i think
let's see, we have 1 huge triangle
the no of smallest triangle is 9+7+5+3+1 = 26
a little bigger triangle .. we have 13, so total is 40 until now
45 is the answer
no .. but quite close
i think 46
Oo... sorry @King 's right i made mistake in above summation
can you explain your approach?
so 45 is rite?
9+7+5+3+1 = 26 .. from this i was able to deduce 46
nos.of small triangles=25 not 26!!@experimentX
9+7=16 5+3+1=9 16+9=25!!
still i cannot come up with general formula ...!
I got 46
no.of triangles=level of @experimentX
hw diya?
Wait letme count again
lol ... quite a matching no.
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!!
no.of triangles with 2 rows of small triangles=10 ...it think this should be 13, aren't we missing inverted triangles?
If overlapping I found 45
yeah!!sry so its 48
not include the inverted ones :(
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there are no inverted ones wid 3 or 4 rows so it has to be 48...i think
so answer is 48!!
@experimentX u der?if u are happy and satisfied wid answer close the question....
i guess 48 is the right answer ...
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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.
floor(n(n+2)(2n+1)/8) where n is the number of triangles on a side in your specific case, n=5
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?
actually, I'm seeing more problems with the solution here isn't there much more going on that we are ignoring?
@philips13 Gave the right answer. \[\huge \lfloor \normalsize \frac{ (n(n+2)(2n+1)}8 \huge \rfloor \]
Oh yeah? Ok thanks, but now I wanna decipher it you seem to be familiar with this theorem FFM :P
I am familiar with almost everything labelled interesting :P http://www.mathematik.uni-bielefeld.de/~sillke/SEQUENCES/grid-triangles
You think we haven't noticed? Where do you get this encyclopedic knowledge?!
Lol, I was kidding. I am just an ordinary guy with some practice :)
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
:)
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
thanks to all for reply!! and finally it's complete!
48 i guess

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