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Five cousins are camping together. Two are from Montana, and three are from Wyoming. Two are Pattersons, and three are Andersons. Irene and Yvonne are from the same state, while Michael and Emily are from different states. Leo and Michael have the same last name; however, Emily and Yvonne do not. The Patterson from Montana awakes in the night to go to the outhouse. What is that cousin's first name?

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Irene and Yvonne are from the same state

They cannot both be from Montana, because then the other three cousins would all be from Wyoming and

Michael and Emily are from different states

would be impossible. Therefore Irene and Yvonne are both from Wyoming. The same reasoning over the next two clues gets us that Leo and Michael are Andersons.

The Patterson from Montana

The Patterson from Montana is not from Wyoming so we can exclude Irene and Yvonne, and not an Anderson so we can exclude Leo and Michael. As there are only 5 cousins and we have excluded 4, we are only left with Emily.

Finally, we can show that the clues are consistent with an example.

     Name:     Emily       Irene       Leo        Michael    Yvonne
     Surname:  Patterson   Patterson   Anderson   Anderson   Anderson
     State:    Montana     Wyoming     Montana    Wyoming    Wyoming

And indeed this example fits all of the clues.

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  • $\begingroup$ @AneesRao, Any part of my answer would spoil a piece of the puzzle if someone saw it. I don't like the idea of hiding an entire post, but I could hide just the example at the end. Readers should expect to have the puzzle spoiled for them if they scroll down to look at the answers, so it is their responsibility not to if they wish to try the puzzle on their own first. However, I usually use spoilers when my answer is right at the beginning of my post. $\endgroup$ – Ben Frankel Oct 7 '15 at 14:21
  • $\begingroup$ Ah well. I did get the same answer. Take an upvote! $\endgroup$ – Anees Rao Oct 8 '15 at 3:03
  • $\begingroup$ Plus one for excellent use of spoiler tags. $\endgroup$ – user3294068 Oct 8 '15 at 15:07
  • $\begingroup$ @user3294068, Actually I didn't use any spoiler tags originally and they were edited in by EngineerToast. I also like it this way though. $\endgroup$ – Ben Frankel Oct 8 '15 at 18:28
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Home states:

Their home states are either Montana or Wyoming, so Irene, Yvonne and one of Michael or Emily must be from Wyoming. Leo is from Montana.

Surnames:

Likewise, Leo, Michael and one of Emily/Yvonne are Andersons, and Irene is a Patterson.

Solution:

Leo and one of Michael/Emily are from Montana, while Irene and one of Emily/Yvonne are Pattersons, with the common name being Emily.

Complete solution:

Leo Anderson - Montana, Michael Anderson - Wyoming, Yvonne Anderson - Wyoming, Emily Patterson - Montana, Irene Patterson - Wyoming

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