how many triangles do you see in figure.

- experimentX

how many triangles do you see in figure.

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- experimentX

##### 1 Attachment

- anonymous

overlapping or no?

- experimentX

overlapping

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## More answers

- anonymous

39?

- King

43 or 45

- King

43-45

- King

44 i think

- experimentX

let's see,
we have 1 huge triangle

- experimentX

the no of smallest triangle is 9+7+5+3+1 = 26

- experimentX

a little bigger triangle .. we have 13, so total is 40 until now

- King

45 is the answer

- experimentX

no .. but quite close

- experimentX

i think 46

- experimentX

Oo... sorry @King 's right i made mistake in above summation

- experimentX

can you explain your approach?

- King

so 45 is rite?

- experimentX

9+7+5+3+1 = 26 .. from this i was able to deduce 46

- King

nos.of small triangles=25 not 26!!@experimentX

- King

9+7=16
5+3+1=9
16+9=25!!

- experimentX

still i cannot come up with general formula ...!

- Diyadiya

I got 46

- King

no.of triangles=level of @experimentX

- King

hw diya?

- Diyadiya

Wait letme count again

- experimentX

lol ... quite a matching no.

- King

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

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

- .Sam.

If overlapping I found 45

- King

yeah!!sry so its 48

- Callisto

not include the inverted ones :(

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- King

there are no inverted ones wid 3 or 4 rows so it has to be 48...i think

- King

so answer is 48!!

- King

@experimentX u der?if u are happy and satisfied wid answer close the question....

- experimentX

i guess 48 is the right answer ...

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- experimentX

still i was looking some sorts of permutations and combinations to this get this answer ... anyway thanks to all who tried.

- anonymous

floor(n(n+2)(2n+1)/8)
where n is the number of triangles on a side
in your specific case, n=5

- TuringTest

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

actually, I'm seeing more problems with the solution here
isn't there much more going on that we are ignoring?

- anonymous

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

- TuringTest

Oh yeah?
Ok thanks, but now I wanna decipher it
you seem to be familiar with this theorem FFM :P

- anonymous

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

- TuringTest

You think we haven't noticed?
Where do you get this encyclopedic knowledge?!

- anonymous

Lol, I was kidding. I am just an ordinary guy with some practice :)

- TuringTest

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

- anonymous

:)

- Callisto

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

thanks to all for reply!! and finally it's complete!

- anonymous

48 i guess

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