I like to tackle the handshake at a dinner party problem for this week!
what we know: 5 couples in the room! couples don't shake hand with each other and two people handshake at most one time.
reading up to here reminds me of a simple graph that with 10 nodes of 5 colors if we say that couples have the same color. There can't be an edge between two same colors and there is at most one edge between two different colors.
I don't know about you but this made a really clear picture of the problem in my head! Turning all our data into something that we can imagine or even simply draw on a paper.
In the following the problem says after a while we no that no two individuals have the same number of handshakes in the room.
we know that one can at most shake hands with 8 people! (10 - partner - him/her self).
if I for eg shake someones hand, this counts for both of us.
at this point there are 9 people with different number of handshakes so we should have 0 to 8 handshakes between them! Since there is someone with 0 handshakes then the person with 8 handshakes has definitely shaken hands with Hilary!
........
next step is to analyze the data in a helpful way
what we know: 5 couples in the room! couples don't shake hand with each other and two people handshake at most one time.
reading up to here reminds me of a simple graph that with 10 nodes of 5 colors if we say that couples have the same color. There can't be an edge between two same colors and there is at most one edge between two different colors.
I don't know about you but this made a really clear picture of the problem in my head! Turning all our data into something that we can imagine or even simply draw on a paper.
In the following the problem says after a while we no that no two individuals have the same number of handshakes in the room.
we know that one can at most shake hands with 8 people! (10 - partner - him/her self).
if I for eg shake someones hand, this counts for both of us.
at this point there are 9 people with different number of handshakes so we should have 0 to 8 handshakes between them! Since there is someone with 0 handshakes then the person with 8 handshakes has definitely shaken hands with Hilary!
........
next step is to analyze the data in a helpful way
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