I am trouble trying to figure out why this is possible or not? In a group of 47 people can each person shake hands with exactly nine other people?

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- Sep 18th 2007, 02:38 PM #1

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- Sep 18th 2007, 03:03 PM #2

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Hello, chadlyter!

I am trying to figure out why this is possible or not?

In a group of 47 people, can each person shake hands with exactly 9 other people?

Let's count the total number of handshakes.

If each of the 47 people shake hands with exactly 9 other people.

. . There will be: .$\displaystyle 47 \times 9 \:=\:423$ handshakes.

But "X shakes hands with Y" and "Y shakes hands with X" is the same handshake.

. . Hence, our number is*twice as large*as it should be.

. . And, obviously, 423 is not divisible by 2.

Therefore, it is not possible.

- Sep 18th 2007, 03:31 PM #3