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Monday, July 28, 2008

The Round Table

Yesterday evening, Helen and her husband invited their neighbours (two couples) for a dinner at home. The six of them sat at a round table. Helen tells you the following:

* "Victor sat on the left of the woman who sat on the left of the man who sat on the left of Anna.
* Esther sat on the left of the man who sat on the left of the woman who sat on the left of the man who sat on the left of the woman who sat on the left of my husband.
* Jim sat on the left of the woman who sat on the left of Roger.
* I did not sit beside my husband."

The Question: What is the name of Helen's husband?

Answer: From the second statement, we know that the six people sat at the table in the following way (clockwise and starting with Helen's husband):

Helen's husband, woman, man, woman, man, Esther

Because Helen did not sit beside her husband, the situation must be as follows:

Helen's husband, woman, man, Helen, man, Esther

The remaining woman must be Anna, and combining this with the first statement, we arrive at the following situation:

Helen's husband, Anna, man, Helen, Victor, Esther

Because of the third statement, Jim and Roger can be placed in only one way, and we now know the complete order:

Helen's husband Roger, Anna, Jim, Helen, Victor, Esther

Conclusion: the name of Helen's husband is Roger.