Question 647255: I have a question along the lines of the "how many handshakes" with a twist. I need to find out how many handshakes would occur if 3 people shook hands at once. I think I've figured out a pattern, but I have no idea how to form an equation that would predict the outcome for various numbers. Here's what I've got so far.
I figured out the trick to it, but I can't come up with an equation. I won't try to explain how I did it, but let me know if this makes sense, and what you think.
Ok.. I'll start with 5. If there are 5 people we figured out there are 10 handshakes. I figured out that if there are 5 people, it would be 6+3+1+0+0=10. The takes into account that the first person would be involved with 6 handshakes, the second person would only get credit for 3 (because the rest would count in the first persons), the third person would get credit for 1 (because the rest would count by person 1 and 2), the fourth and fifth persons would not get credit for any because theirs would have been counted by the first 3 people.
Now look at 6 people. There equation would be 10+6+3+1+0+0=20. Same idea. First person gets credit for 10 handshakes, second gets credit for 6...and so on.
7 people equation. 15+10+6+3+1+0+0=35. You get the idea.
Now matter what the last 2 people always come up as zero. If we drop the last two zeros and flip the equation for the above example the equation would be 1+3+6+10+15=35. Now the difference between 1 and 3 is 2, the difference between 3 and 6 is 3, the difference between 6 and 10 is 4. Basically if we use the number of people in the handshake, take away two and then add consective integers to the equation it will always work. Does this make sense?
8 people would look like 1+3+6+10+15+21=56.
Now my question is what should the equation look like?
Thanks for any help you can give me.
Laurie
Answer by aaronwiz(69)   (Show Source):
You can put this solution on YOUR website! Hi, my name is Aaron I am in 10th grade and im in honors trig/pre-calc.
Although I dont understand how you arrived at your result (im to tired), I can tell you the equation will be a parabola. Try plugging points into a parabola in vertex form. Best of luck
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