Science & Mathematics - 29 August 2006

Hi ,
I have this logic puzzle I've been trying to solve for quite some time and I'd appreciate any help: It goes like this:
You have a round table with 20 seats all around it . You sit 10 men and 10 women in a totally random order. In the middle there is a round cake divided into 20 slices where each slice is in front of one person sitting around the table . Some of the slices have a cherry on them and some don't. The number and the arrangment of cherries is also totaly random (the number can't be more then 20). Men are happy if they see a cherry on the slice in front of them and women are happy if they see a slice without a cherry.
it's a prove or dismiss question (I think the direction goes towards proof). The taurem is "for any arrangment of people around the table and of cherries on the cake we should be able to make at least half the people around the table happy only by rotating the cake (as many degrees as we want)" . I'm looking for a clear proof of a dismissing example

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