The question is how many handshakes would be in a group if everyone were to shake each other's hands twice. P stands for people(in a group), HS stands for handshakes. I wrote down the the number of people in a group first. N just happened to be the same number as people in a group. then I started to evaluate my information and start finding the handshakes. I used shapes to find the handshakes, crossing lines to represent handshakes. By the fourth group, I had already established a pattern but I used the fifth group to check my hypothesis and as you can see I didn't draw a shape for the sixth group and that is because I had proven my hypothesis thus following the pattern. Finally, I looked back at the pattern and wrote it in function form(luckily for me the N=P so it was easier for me). My conclusion was that N(N-1)= F(N). Lets test it 2(2-1)=2 which happens to be the number of HS. Maybe that was a coincidence lets try a bigger number 5(5-1)=20. Wow! I challenge you to prove me wrong on this hypothesis. If you can't, you know why. Stay Classy!
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