Wednesday, February 06, 2008

The Maths of Chinese New Year

Today is Chinese New Year’s eve; our company has a mini ‘makan’ celebration before it closed at noon when all employees go back for a long long weekend and celebrations.

It is common for each of us colleagues to greet one another, exchanging handshakes at such occasion.

Obviously I could not afford to shake hands with each of the colleagues present in this crowd of 25. If everyone is to shake hands with one another, say for our crowd of 25 and each handshake takes 5 seconds, it would need a total of 25 minutes for all colleagues to shake hands with one another!

Actually this phenomenon is commonly known as the ‘handshake problem’ and one can read about it in the internet. I can give a simple mathematical explanation here:

Assuming that there are n people and each person is to shake hands with one another.

Visualise this n number of people standing in a row, the 1st person stands out facing opposite the remaining members and shakes hand with the remaining (n-1) members and leaves the row.

Next the 2nd person stands out, again facing the remaining members and shakes hand with the remaining (n-2) members and leaves the row.

Then the 3rd person stands out, again facing the remaining members and shakes hand with the remaining (n-3) members and leaves the row.

This continues till the 2nd last person (this will be the (n-1)th) person stands out, again facing the remaining members and shakes hand with the remaining 1 member and leaves the row.

There will be no more handshakes after that.

The number of handshakes will be the summation of all the handshakes commencing from the 1st person to the 2nd last person.

Thus to summarise, for the rth person, he will experiences (r-1) handshakes, i.e: The 1st
person (nth person, r = n) will experience (n-1) handshakes, and the last person (r =1 ) will experience 0 handshakes.

Summarizing (r-1) from r = 1 to r = n and using secondary school summation techniques, we arrived at (n squared-n)/2 handshakes!

Thus if a group of 25 people is to shake hands with one another, there would be a total of 300 handshakes involved!

Maybe you can give this simple mathematical problem to your teenager relatives in Sec 3 or 4 during visiting and saves the angbao if they cannot solve it.

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