Handshake !
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
The answer is 12.
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8 solutions
Everybody makes only 1 handshake with everbody else.
Thus, we can assume that there were n people at the party. So, the number of handshakes were 6 6 .
2 n ( n − 1 ) = 6 6
n ( n − 1 ) = 6 6 × 2
n ( n − 1 ) = 1 3 2
n 2 − n = 1 3 2
n 2 − n − 1 3 2 = 0 (Can be solved by quadratic equation or middle term splitting!)
n 2 + 1 1 n − 1 2 n − 1 3 2 = 0 (Middle term splitting)
n ( n + 1 1 ) − 1 2 ( n + 1 1 ) = 0
( n − 1 2 ) ( n + 1 1 ) = 0
So, n = 1 2 or n = − 1 1
But n = − 1 1 because people cannot be in negative integers!
Thus, n = 1 2 . So, the answer is 1 2 .
n(n-1)/2 = 66 n = 12
I don't understand why this question is repeated so many times.I have solved this question at least 15-20 times.
ISN'T 65C2
n(n-1)/2!
sigma (n-1)=66 =>n(n-1)/2=66 => n2-n-132=0 =>(n-12)(n+11)=0 therefore n=12
12 person because persone number 1 will hand shake with 11 and person number 2 will hand shake with 10 ......... 11+10+9+8+7+6+5+4+3+2+1=66
liked
ans is 12 ...... cuz if 12 people are there then one will hand shake with 10 people and so on it will 65 shakes and 1 is of 12th person :)
liked
1+2+3+4+5+6+7+8+9+10+11=66 The first person shakes hands with all the other people except himself. So, we have to add one to 11, making 12.
1+2+3+4+5+6+7+8+9+10+11=66 I added 1 to 11 and got12
Its just number of ways of selecting two persons from 'n' number of persons which is equal to n*(n-1)/2=66. On solving you will get n=12
C(n,2)=66
n (n-1) (n-2)! / (n-2)! 2! = 66
n(n-1)=132
n^2-n-132=0
(n-12)(n+11)=0
n adalah jumlah manusia, berarti kudu positif ;) dadine n sing memenuhi 12 ^_^