## experimentX Group Title how many triangles do you see in figure. 2 years ago 2 years ago

1. experimentX Group Title

2. myko Group Title

overlapping or no?

3. experimentX Group Title

overlapping

4. myko Group Title

39?

5. King Group Title

43 or 45

6. King Group Title

43-45

7. King Group Title

44 i think

8. experimentX Group Title

let's see, we have 1 huge triangle

9. experimentX Group Title

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

10. experimentX Group Title

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

11. King Group Title

12. experimentX Group Title

no .. but quite close

13. experimentX Group Title

i think 46

14. experimentX Group Title

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

15. experimentX Group Title

16. King Group Title

so 45 is rite?

17. experimentX Group Title

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

18. King Group Title

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

19. King Group Title

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

20. experimentX Group Title

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

I got 46

22. King Group Title

no.of triangles=level of @experimentX

23. King Group Title

hw diya?

Wait letme count again

25. experimentX Group Title

lol ... quite a matching no.

26. King Group Title

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 Group Title

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

28. .Sam. Group Title

If overlapping I found 45

29. King Group Title

yeah!!sry so its 48

30. Callisto Group Title

not include the inverted ones :(

31. King Group Title

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

32. King Group Title

33. King Group Title

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

34. experimentX Group Title

i guess 48 is the right answer ...

35. experimentX Group Title

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

36. philips13 Group Title

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 Group Title

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 Group Title

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

39. FoolForMath Group Title

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

40. TuringTest Group Title

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

41. FoolForMath Group Title

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

42. TuringTest Group Title

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

43. FoolForMath Group Title

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

44. TuringTest Group Title

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 Group Title

:)

46. Callisto Group Title

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 Group Title

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

48. kr7210 Group Title

48 i guess