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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Telegram hopes to raise $1bn with a convertible bond private placement
The super secure UAE-based Telegram messenger service, developed by Russian-born software icon Pavel Durov, is looking to raise $1bn through a bond placement to a limited number of investors from Russia, Europe, Asia and the Middle East, the Kommersant daily reported citing unnamed sources on February 18, 2021.The issue reportedly comprises exchange bonds that could be converted into equity in the messaging service that is currently 100% owned by Durov and his brother Nikolai.Kommersant reports that the price of the conversion would be at a 10% discount to a potential IPO should it happen within five years.The minimum bond placement is said to be set at $50mn, but could be lowered to $10mn. Five-year bonds could carry an annual coupon of 7-8%.
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