Q: How many handshakes are there if 100 people all shake hands?

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4950

45 handshakes

You could never guarantee 1000 handshakes because the people may choose not to shake hands! If each person did shake hands with everyone else, then 46 people would suffice.

55 PeopleHandshakes10213346510615721828936104511551266

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

Related questions

12

4950

45 handshakes

190

20*19/2 = 190

You could never guarantee 1000 handshakes because the people may choose not to shake hands! If each person did shake hands with everyone else, then 46 people would suffice.

66

55 PeopleHandshakes10213346510615721828936104511551266

Each person will shake hands with every other person, except himself. If there are 25 people, each person will shake hands with 25-1 people, or 24. The number of times each person will shake hands with another, will be 25x24. The number of handshakes will be half of that, as each handshake is between two persons. The formula, in other words, is x(x-1)/2, where x is the number of people. With 25 people, it will be 25x24/2 = 300 handshakes.

So, there will be 3 handshakes among the 3 people at the party.

Sixty-six unique, distinct handshakes.

11*10/2 = 55