It is known that the number of handshake within a group of people is the sum of integer between 1 and (number of people in the group - 1). Say there are persons A, B, C, D and E (5 people) in a group and all shook hands, the number of handshakes will be sum of integers between 1 and (5-1) i.e. 1 + 2 + 3 + 4 = 10.
Let's confirm this: - Person A shakes B, C, D, and E (4 handshakes) - Person B shakes C, D, and E (no need to shake A again because A already shook him) (3 handshakes) - Person C shakes D and E (2 handshakes) - Person D shakes E (1 handshake) - Person E don't have to shake anybody, they have all shook him
So, 4 + 3 + 2 + 1 = 10
And also we know that the sum of 1 to n = (n(n+1)) ÷ 2. Say you want to add 1 to 10 that will be = (10 x (10 + 1)) ÷ 2 = (10 x 11) ÷ 2 = 110 ÷ 2 = 55 (also try it with your calculator)
With this information, we now know the number of handshakes in a group of 120 people will be 1 + 2 + 3 + ... + 119
But we don't have to add sequentially like that, we just do (119 x 120) ÷ 2 = 14280 ÷ 2 = 7140
It is known that the number of handshake within a group of people is the sum of integer between 1 and (number of people in the group - 1). Say there are persons A, B, C, D and E (5 people) in a group and all shook hands, the number of handshakes will be sum of integers between 1 and (5-1) i.e. 1 + 2 + 3 + 4 = 10.
Let's confirm this: - Person A shakes B, C, D, and E (4 handshakes) - Person B shakes C, D, and E (no need to shake A again because A already shook him) (3 handshakes) - Person C shakes D and E (2 handshakes) - Person D shakes E (1 handshake) - Person E don't have to shake anybody, they have all shook him
So, 4 + 3 + 2 + 1 = 10
And also we know that the sum of 1 to n = (n(n+1)) ÷ 2. Say you want to add 1 to 10 that will be = (10 x (10 + 1)) ÷ 2 = (10 x 11) ÷ 2 = 110 ÷ 2 = 55 (also try it with your calculator)
With this information, we now know the number of handshakes in a group of 120 people will be 1 + 2 + 3 + ... + 119
But we don't have to add sequentially like that, we just do (119 x 120) ÷ 2 = 14280 ÷ 2 = 7140
Answer: 7140
BY Riddles Repository - Answers
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