Handshake Problem with a much larger In Discussion Post 2 we revisited The numbe
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Handshake Problem with a much larger In Discussion Post 2 we revisited The number than was explored in the Guided Activity in Module 2. In that discussion post, we learned that if U.S. Bank Stadium, in Minneapolis, Minnesota (where Super Bowl Fifty-two is planned to be held in February of 2018) was filled to capacity with 66,655 fans, then the number of handshakes (or greetings) that would take place if all of the fans participated in "The Handshake Problem" would be 2,221,411,185 ha ndshakes, assuming this was even possible I R1s Now, suppose that hypothetically each handshake took 2 seconds. How long (to the nearest year) would these handshakes have taken? Upload a file with a completely detailed solution to this problem. Be sure to show or fully explain your entire thought process. Again, as in the previous questions, just providing an answer without any work to justify it will be worth no more than 0.5 point.Explanation / Answer
Lets take a small example of 10 players doing handshakes among themselves to derive the Handshake problem.
If, for example, 10 players met, the first player will make 9 handshakes, the second makes 8, the third makes 7 and so on until the tenth finds he has already made handshakes with everyone and so makes no more.
This gives 9+8+7+6+5+4+3+2+1+0 handshakes and this is 45.
But look at the sequence... it is the 9th triangular number.
The formula for the Tth triangular number is T(T+1)/2
With the handshake problem, if there are n people, then the number of handshakes is equivalent to the (n-1)th triangular number.
Subsituting T = n-1 in the formula for triangular numbers, we can deduce a formula for the number of handshakes between n people:
Number of handshakes = (n-1)(n)/2
Hence, total number of Fans=66655
Total number of handshakes=66655*(66655-1)/2=2221411185
Now each handshake takes 2 seconds then total time take = 2221411185*2=4442822370seconds
Or 74047039.5 minutes or 1234117.325 hours or51421.5552083 days or approximately 141 years.
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