4950
20 ; 80 (assuming they shake both hands)
4950
Since it takes two to shake hands, no odd number of people can handshake, since one must be left out. Therefore 99 people cannot shake hands. Unless "handshake" means something unusual here, which seems unlikely, as it is the only handshaking activity where you can count the handshakes. * * * * * What utter nonsense! 3 people: A, B and C can shake hands. AB shake hands, AC shake hands and BC shake hands. And the last time I looked 3 was still classified as an odd number. The correct answer is 99*98/2 = 4851
36. Everybody shakes 8 hands but each shake counts for 2 people. So 9*8/2=36.
4950
So, there will be 3 handshakes among the 3 people at the party.
15
10 times
3. AB, BC and CA.
The first person must shake hands with 5 other people. The next must shake hands with 4 other people, since you exclude the first person. Keep going and you'll find that there will be 5+4+3+2+1=15 handshakes. Numbers like this are called triangular numbers.
12
20 ; 80 (assuming they shake both hands)
4950
Sixty-six unique, distinct handshakes.
Since it takes two to shake hands, no odd number of people can handshake, since one must be left out. Therefore 99 people cannot shake hands. Unless "handshake" means something unusual here, which seems unlikely, as it is the only handshaking activity where you can count the handshakes. * * * * * What utter nonsense! 3 people: A, B and C can shake hands. AB shake hands, AC shake hands and BC shake hands. And the last time I looked 3 was still classified as an odd number. The correct answer is 99*98/2 = 4851
36. Everybody shakes 8 hands but each shake counts for 2 people. So 9*8/2=36.