Not the normal handshakes

Probability Level 3

In a party 2015 people get together and shake hands with every person except the ones sitting adjacent to them supposing them to sit in a circle. Each person shakes hand with each other but only once.How many handshakes took place?

The answer is 2027090.

3 solutions

Satyajit Ghosh
Jul 24, 2015

A great solution by my friend @Kushagra Sahni . Consider the problem as a polygon with 2015 corners. Now what is a diagonal? Line joining 2 corners except the adjacent ones. So just applying n(n-3)/2 you will get the answer

Thanks Bro

Kushagra Sahni - 5 years, 10 months ago

How did you think of such a solution? It's commendable! awesome

Raven Herd - 5 years, 10 months ago

It's Just like yours, only a bit quicker. U also did n(n-3)/2 didn't you. Your solution is also very nice .

Kushagra Sahni - 5 years, 10 months ago

@Kushagra Sahni – C'mon modesty has a height! My solution is a common one .I just went with the rhythm of the question ,you thought out of the box. That's brilliance!

Raven Herd - 5 years, 10 months ago

@Raven Herd – Thanks Mate. Where are u from by the way, which state?

Kushagra Sahni - 5 years, 10 months ago

@Kushagra Sahni – I think you must open your grade 3 SST book .They teach there that Lucknow is in Uttar Pradesh...

Raven Herd - 5 years, 10 months ago

@Raven Herd – I never opened your profile. I just saw you in the comments so only India was written that's why I asked.

Kushagra Sahni - 5 years, 10 months ago

Hey....this problem is similar to a problem which came in $NMTC$ $2014$ paper.

Akshat Sharda - 5 years, 9 months ago

Raven Herd
Jul 24, 2015

Consider a person A among these 2015 people sitting in a circle .A cannot shake hands with her neighbours and ofcourse with herself so in a total 1 person shakes hand with 2015-3 =2012 people ,so A has to do 2012 handshakes and there are 2015 people in total so total number of handshakes =2012 2015 but consider another person B who will shake hands with A 2 times ;once done by A and another time by himself so we have counted 2 times .Thus the total number of handshakes is 2012 2015/2=2027090

Nice method :)

Satyajit Ghosh - 5 years, 10 months ago

Panshul Rastogi
Aug 15, 2015

come on Kushagra bhaiyya, ma'am told us the solution !!

He told me the way just after the quiz and it was his thinking.

Satyajit Ghosh - 5 years, 10 months ago

Bhai quiz dene k baad maam k paas kab gaya main? Mera answer sahi tha to maam k paas kyu jaaunga main?

Kushagra Sahni - 5 years, 10 months ago

Not the normal handshakes

The answer is 2027090.

3 solutions

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