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
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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.
If you multiply anything by 2 it always comes out even. So if people make 35 handshakes, we multiply it by 2 and we get 70 people. This will work with any different number of handshakes, odd or even.
The answer is 15 people. Each shook hands with 14 others, and there are half that many handshakes (pairs). The total number of pairs (distinct handshakes) within the group is defined by the formula T = [n!/(n-2)!] /2 Given T = 105 we get n!/(n-2)!=210 which implies n(n-1)=210 on solving we get n=15
15 (15 * 15 - 15)/2 = 105