Handshakes

How many Handshakes?

    As I sat in meeting this morning I looked around. We were ten people. I reflected that last week we were only three people, though it was an excellent meeting in all respects.  At the end, lacking an elder, we had all shaken hands with each other. 

    Today there were ten of us. The age-old problem came to mind, of how many handshakes would be involved this time if we all shook hands with each other. (I remembered the question from schooldays some 65 years ago). 

    But, with a gratifying flash of insight, the answer came to me; there would have to be 45 handshakes to be complete. The clue came from our unusually small meeting of the previous week. Three people each shook two hands making six greetings. But each shake met two of those six greetings. Answer = three. 

    I could put it this way. For n people, there would be:
                 n x (n-1)/2 
shakes. So for 10 people each greeting 9 others (as you do not greet yourself), so 90 greeting; but only 45 shakes.

Number of people (n)        Greetings            Shakes

        1                                    0                           0
        2                                    2                           1
        3                                    6                           3
        4                                   12                          6
        5                                   20                        10

    I am pretty sure I am right. But concede that it does not amount to 'Ministry'. Nor 'Afterwords', really. Perhaps I should keep it for the monthly newsletter.