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Question Number 911 by 112358 last updated on 22/Apr/15

E i g h t p e o p l e a r e s e a t e d a r o u n d

a c i r c u l a r t a b l e . E a c h p e r s o n

m u s t s h a k e {e v e r y o n e}^{'} s h a n d b u t

t h e y m u s t n o t s h a k e h a n d s w i t h

t h e t w o p e r s o n s s e a t e d a t t h e i r s i d e s .

H o w m a n y h a n d s h a k e s o c c u r ?

Answered by prakash jain last updated on 22/Apr/15

This will same as number of diagonals in

an octagon .

\frac{8 \times 5}{2} = 20

Commented by 112358 last updated on 23/Apr/15

W o u l d i t b e p o s s i b l e t o g e n e r a l i s e

t h i s p r o b l e m w h e r e t h e r e a r e n

p e o p l e a n d m n u m b e r o f p e r s o n s

s e a t e d o n b o t h s i d e s o f e a c h

p e r s o n w i t h w h o m h a n d s c a n n o t

b e s h a k e n ?

Commented by prakash jain last updated on 23/Apr/15

\frac{n \times (n - 2 m - 1)}{2}

2 m, m p e o p l e o n e i t h e r s i d e

1, s e l f

So each point is connected with n - (2 m + 1)

points .

Divide by 2 for counting each line twice .