If-four-people-all-said-HELLO-to-each-other-once-how-many-times-would-the-word-HELLO-be-spoken-

Question Number 5897 by sanusihammed last updated on 04/Jun/16

I f f o u r p e o p l e a l l s a i d H E L L O t o e a c h o t h e r o n c e . h o w m a n y

t i m e s w o u l d t h e w o r d H E L L O b e s p o k e n ?

Answered by FilupSmith last updated on 04/Jun/16

p e r s o n 1 t a l k s t o 3 p e o p l e

p e r s o n 2 t a l k s t o 2 p e o p l e

p e r s o n 3 t a l k s t o 1 p e o p l e

e v e r y o n e h a s t a l k e d t o p e r s o n 4 .

∴ = 3 + 2 + 1

t i m e s t a l k e d = 6

Commented by FilupSmith last updated on 04/Jun/16

f o r n p e o p l e :

t i m e s t a l k e d = \underset{i = 1}{\sum^{n - 1}} i

= \frac{n^{2} - n}{2}

Commented by prakash jain last updated on 04/Jun/16

I think if two person say hello both of them

will need to speak .

so word hello will be spoken 6 \times 2 = 12 times

Commented by FilupSmith last updated on 05/Jun/16

i f e v e r y o n e s a i d h e l l o t o e a c h o t h e r,

b u t n o t w o p e o p l e s a y h e l l o t o e a c h o t h e r

m o r e t h a n o n c e :

(1) s a y s h e l l o t o 2 3 a n d 4

(2) s a y s h e l l o t o 3 a n d 4 (1 a l r e a d y s e i d h e l l o)

3 says hello to 4

everyones talked to 4 so 4 does nothing

= 3 + 2 + 1 = 6

this is true only if they talk to each other

once only .

Commented by FilupSmith last updated on 05/Jun/16

i f 4 p e o p l e s a i d h e l l o t o e a c h o t h e r

w i t h o u t r e s t r i c t i o n, e a c h p e r s o n

s a y s h e l l o (n - 1) t i m e s f o r n p e o p l e

= n (n - 1)

= 4 (3)

= 12