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At a dance once there were three women there who seemed to be without partners. Only they were in a group and the task of going up to a group of three and asking one to dance was too daunting. Plus, if you get turned down, how are the other two going to like being 2nd choice?
I think the Nash solution is to ask your 2nd choice. She is likely to accept, given that she expects to be passed over for her prettier friend.
I suppose I could have asked the whole group if there was one of them who wanted to dance with me.
It is tough though. The only time I have any luck is when I have a sister, sister in law, cousin, or co-worker there who will dance with me. Although I did connect with a group of three girls and one guy. When the three girls got up to dance, I started a conversation with the guy.
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