Mathematics Blog
This is the first in an occasional blog where I try and
recall the mathematics which I have learnt and apply it in situations.
…then eventually, I will try and explain in a longer manner
where it could go and where applicable why I came up with the problem.
A reunion took place with 8 persons. If each person hugged
everyone else once, how many hugs (of two persons) took place?
The answer is of course 8C2 -= 8!/(6!
2!) = 8 ×
7 / (2 ×
1) = 28
However if the eight consist of three married couples and
two single people, and the spouses did not hug each other, the number of hugs
becomes 28 – 3 = 25
In general, if there are n
persons including r couples implies nC2
– r hugs took place.
The longer discussion
I thought about this when wondering when 8 of us met up how many
hugs there would be. I of course calcualted 28 then I wondered why there was not
28 hugs and then I realised we arrived in three groups…one on his own, two
couples together and I and another couple. This was followed by the fact the
couples did not hug… So you may be interested to work out how many hugs I needed
to do and see once we all met…assuming those who arrived did not hug those they
arrived with! It might also be worth wondering how long it took to hug.
In general Discrete Mathematics has plenty of applications.
The mathematics would of course refer to pairs etc or perhaps unordered pairs.
Also threesomes or triples and other n-tuples could be considered.
