You were invited to join a discussion for the future of learning, there are 20 people there (including you) and everyone's going to handshake each other once. How many handshakes are going to occur?
Though many may think at first that the answer is 380, that answer is incorrect.
So, How did we reach the answer of 380?
there are 20 people and everyone is going to handshake each other, but they can't handshake themselves. So many people may think "19x20=380".
Imagine this, you are in a group of 4 and you are going to handshake everyone once.
you handshake 3 people, the second handshakes 2 and the third handshakes 1, while the fourth doesn't handshake anyone for he/she already shook the others hands. making it only 6 handshakes.
How do you solve this? many at this moment "19+18+17... 3+2+1". how do you simplify this?
There are 2 tricks, The simplest one is working on 3 smaller cases and trying to find a pattern.
4 people = 6 handshakes. And if we used the wrong way, we get 12 (3x4) cause you can't handshake yourself.
5 people = 10 handshakes. Using the same wrong technique, we get 20 (4x5)
6 people = 15 handshakes. Again with the same technique, we get 30 (5x6)
Can you see a pattern? if we use the same technique, we always get twice more than the correct answer.
19x20 =190
2
This is the second trick. you split 20 into 2 groups, 1-10 and 11-20 (no, this is not subtraction).
You add the smallest number of the smaller group to the largest number of the largest group, 1+20=21.
Then you do the same thing again only with the second smallest and the second largest, 2+19=21
Then the same thing with the 3rd, 3+18=21.
Can you see the pattern? You multiply the answer with the largest number in the smaller group, which would be 10 and you get the answer of 210, but you can't handshake yourself, 210-20=190.
Right now I'm stuck in a problem and I only have 3 minutes to solve it. What's that problem you ask? I blogged about the wrong thing...
