experimentX
how many triangles do you see in figure.
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experimentX
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5
myko
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0
overlapping or no?
experimentX
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overlapping
myko
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39?
King
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43 or 45
King
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43-45
King
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44 i think
experimentX
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let's see,
we have 1 huge triangle
experimentX
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the no of smallest triangle is 9+7+5+3+1 = 26
experimentX
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a little bigger triangle .. we have 13, so total is 40 until now
King
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45 is the answer
experimentX
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no .. but quite close
experimentX
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i think 46
experimentX
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Oo... sorry @King 's right i made mistake in above summation
experimentX
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can you explain your approach?
King
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so 45 is rite?
experimentX
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9+7+5+3+1 = 26 .. from this i was able to deduce 46
King
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nos.of small triangles=25 not 26!!@experimentX
King
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9+7=16
5+3+1=9
16+9=25!!
experimentX
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still i cannot come up with general formula ...!
Diyadiya
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I got 46
King
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no.of triangles=level of @experimentX
King
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hw diya?
Diyadiya
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Wait letme count again
experimentX
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lol ... quite a matching no.
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!!
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?
.Sam.
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If overlapping I found 45
King
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yeah!!sry so its 48
Callisto
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not include the inverted ones :(
King
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there are no inverted ones wid 3 or 4 rows so it has to be 48...i think
King
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so answer is 48!!
King
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@experimentX u der?if u are happy and satisfied wid answer close the question....
experimentX
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i guess 48 is the right answer ...
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.
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
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?
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?
FoolForMath
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@philips13 Gave the right answer.
\[\huge \lfloor \normalsize \frac{ (n(n+2)(2n+1)}8 \huge \rfloor \]
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
TuringTest
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You think we haven't noticed?
Where do you get this encyclopedic knowledge?!
FoolForMath
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Lol, I was kidding. I am just an ordinary guy with some practice :)
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
FoolForMath
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:)
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
experimentX
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thanks to all for reply!! and finally it's complete!
kr7210
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48 i guess