Math Is Fun Forum

Dharshi

Member

Registered: 2006-10-31

Posts: 56

Discrete maths

Use the Handshake Theorem  to solve the following problem. Suppose that you arrive
at a gathering of 9 people. Suppose that upon your arrival, you learn two facts: that 36 handshakes
have already taken place and that every person participated in the same number of handshakes, h.
How many hands did each of the 9 people shake? (Find h).

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Discrete maths

Hi;

Easy enough by combinatorics. Each of the nine people shook 8 hands. (9*8)/2 = 36 handshakes.

The handshake lemma says the sum of the degree of the vertices of a graph is equal to twice the number of edges.

Draw a graph of the handshakes and apply the theorem.

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