## experimentX 3 years ago how many triangles do you see in figure.

1. experimentX

2. myko

overlapping or no?

3. experimentX

overlapping

4. myko

39?

5. King

43 or 45

6. King

43-45

7. King

44 i think

8. experimentX

let's see, we have 1 huge triangle

9. experimentX

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

10. experimentX

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

11. King

45 is the answer

12. experimentX

no .. but quite close

13. experimentX

i think 46

14. experimentX

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

15. experimentX

can you explain your approach?

16. King

so 45 is rite?

17. experimentX

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

18. King

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

19. King

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

20. experimentX

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

I got 46

22. King

no.of triangles=level of @experimentX

23. King

hw diya?

Wait letme count again

25. experimentX

lol ... quite a matching no.

26. 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!!

27. experimentX

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

28. .Sam.

If overlapping I found 45

29. King

yeah!!sry so its 48

30. Callisto

not include the inverted ones :(

31. King

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

32. King

so answer is 48!!

33. King

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

34. experimentX

i guess 48 is the right answer ...

35. experimentX

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

36. philips13

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

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

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

39. FoolForMath

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

40. TuringTest

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

41. FoolForMath

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

42. TuringTest

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

43. FoolForMath

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

44. 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

45. FoolForMath

:)

46. 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

47. experimentX

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

48. kr7210

48 i guess