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Answer» HERE IS YOUR ANSWER. .....
ANSWER IS 12...
Explanation:
Let's start with small numbers of people and handshakes and move from there. I'll represent people with LETTERS to show the handshakes:
If we have 2 people, there is 1 handshake (AB).
If we have 3 people, there are 3 handshakes
(AB, AC, BC).
If we have 4 people, there are 6 handshakes
(AB, AC, AD, BC, BD, CD).
If we have 5 people, there are 10 handshakes
(AB, AC, AD, AE, BC, BD, BE, CD,
CE, DE)
.
See that we can express the number of handshakes as the sum of CONSECUTIVE positive integers, starting with 1, i.e.
1 + 2 + 3 + ... + (n − 1) and the number of people present is n
Let's test this with 5 people. We have
1 + 2 + 3 + 4 = 10 handshakes.
n − 1 = 4 ⇒ n = 5 which is the number of people.
So what we need to do is add up to 66 and we'll be able to find the number of people:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
+ 10 + 11 = 66 ⇒
⇒ n − 1 = 11 ⇒ n = 12
HOPE IT HELPS!!!
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