Answer : 12 people.
The 1st person can't shake hands with him/herself so has 11 handshakes, the 2nd person has 10 ....and so on.
The total is 11 + 10 + ....+ 3 + 2 + 1 = 66.
Another way is to use the formula to sum a range of consecutive integers from 1 to n.
The Sum = ½n(n - 1)
In this case, we can put, ½n(n - 1) = 66 then, 132 = n2 - n : n2 - n - 132 = 0
This equation can be factored, (n + 11)(n - 12) = 0
As we only require a positive integer solution, this is when n - 12 = 0, n = 12.
107 unique handshakes will be exchanged
This is a variation on the handshake problem which say if there are n people at a party and every one shakes hands with every other one, how many handshakes are there? It is well know that kisses in fact are cleaner than handshakes which to tend to pass diseases. So thanks for a cleaner version of this classic math problem! n(n-1)/2 is the formula for the number of handshakes OR kisses for n people at a party. If you case, 15x14/2 which is 15x7 or 105.
Assuming that each person makes a shaking partnership just once and no one shakes there own hand,Consider the situation. The eight people are in a line. The first person goes down the line shaking hands with everyone else so he shakes hands 7 times. He then sits down. The second person shakes hands with everyone left in line, six handshakes, and sits down, He has no need to shake ands with the sitting man as they already shook. The remainder follow the same procedure, shaking hands with those standing, not shaking with those sitting. The last man standing shakes with no one as no one is standing and sitsThe sum of hand shakings initiated by each person is 7+6+5+4+3+2+1+0 = 28
try it out in real life, or draw it out. Basically if you have 5 people at the party and every one shakes hands (if this is what you mean) you could do this: draw 5 dots in a circle, and draw a line between every single dot, count the lines and voila you have your answer
28 people each shook hands once...?
371
38
There will be 28 handshakes. If you ask each person how many handshakes they had they will tell you 7 making 7 x 8 = 56 handshakes in all. But every hand involves two people, so every handshake has been counted twice, thus there are 56 / 2 = 28 handshakes in all.
If that happens you have to times ninexten and the answer would be 90 handshakes
21 handshakes
If there are seven people, then the number of handshakes is 7*6/2 = 21
Sixty-six unique, distinct handshakes.
There were ten people at the party. This is a triangular sequence starting with two people: 1, 3, 6, 10, 15, 21, 28, 36, 45, etc. There's an equation for this. With n people at the party, the number of handshakes is n(n-1)/2.
107 unique handshakes will be exchanged
There were 40 people at the party. Let n be the number of people at the party. Each person shakes hands with every other person, so each person shakes hands with (n - 1) people, a possible total of n(n - 1) handshakes. But when person A shakes hands with person B, B also shakes hands with A, so each handshake would be counted twice. → number_of_handshakes = n(n - 1)/2 total number of handshakes is 780 → n(n - 1)/2 = 780 → n(n - 1) = 1560 → n^2 - n - 1560 = 0 As 1560 is negative, one factor is positive and one is negative, so we need the factor pair of 1560 which has a difference of 1, namely: 39 x 40 → (n - 40)(n + 39) = 0 → n = 40 or -39 There cannot be a negative number of people → there are 40 people present.
So, there will be 3 handshakes among the 3 people at the party.
29 People including You.