The 9 people at a conference shook hands exactly once with each other before the tenth person arrived.
The tenth person shook hands with some of these 9 people. If a total of 40 handshakes took place, with how many people did the tenth person shake hands?
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The sum of all the digits from n-1 down to 1 is known as a triangular number: T(n-1); there is a formula for Tn…
Tn = n (n + 1) / 2 hence:
T(n - 1) = (n - 1)(n) / 2
In the case of nine people, n = 9 so…
T(n - 1) = T8 = 8 (9) / 2 = 36 handshakes
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