Find the digit sum of the number of triangles formed by intersecting diagonals of an 8-sided figure? :D
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This is fallacious..
A complete answer here: https://cs.uwaterloo.ca/journals/JIS/sommars/newtriangle.html
The number of triangles is 632 all in all. 6+3+2=11
what does it mean
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It means that there are 632 triangles all in all. It includes the small triangles that are formed by intersecting diagonals from vertices to the other. Do I answer your question? :)
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@Chinmay Raut – do you know the problems such as count the number of squares? This problem is like that. You need to count even the smallest of the triangles :)
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Oh kk ....... [you could have told that in the first place :-P ] ty anyways :-)
Couldn't this problem be solved by Permutation and Combination? Just guessing. Can someone answer this? @Anugrah Agrawal
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Hey @Nikhil Tandon I have solved it by permutations and combinations...please take a look at it as well...
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A n e i g h t s i d e d f i g u r e c o n t a i n s 8 v e r t i c e s , n o n e o f w h i c h a r e c o l i n e a r . S o , t h e q u e s t i o n r e d u c e s t o t h e f o r m a t i o n o f t r i a n g l e s f r o m 8 p o i n t s i n a p l a n e , n o n e o f w h i c h a r e c o l i n e a r . S i n c e t h e r e a r e 8 p o i n t s , a n d t h r e e p o i n t s a r e r e q u i r e d t o c o n s t r u c t a t r i a n g l e . T h e r e f o r e , t h e n u m b e r o f w a y s i n w h i c h t h e s e 3 p o i n t s c a n b e s e l e c t e d i s g i v e n b y c o m b i n a t i o n : C ( 8 , 3 ) = 5 ! 3 ! 8 ! = 5 ! 3 × 2 8 × 7 × 6 × 5 ! = 5 6 S u m o f d i g i t s = 5 + 6 = 1 1
CHEERS!!