Question: Two sheriffs are working on a case to find one culprit. There were initially 8 suspects; through independent work, each sheriff has narrowed this down to a list of 2. Because they are good sheriffs, they can be sure that both of their lists contain the culprit. They plan to make a phone call tonight to see if they can combine their information to find the culprit. However, the locals (who know the 8 suspects, but neither of the narrowed lists) have tapped their phone line. If the locals can figure out the culprit based on this phone call, then they will lynch him before he can be brought to justice. 

How can the sheriffs conduct their conversation so that they can both deduce the culprit, when possible\*, but the locals can't?

\*If the sheriffs have the same list of 2 suspects, then they won't be able to deduce the culprit. As long as their lists are different, they can. The lists cannot be disjoint, since they both contain the unique culprit.

Source: *Mathematical Puzzles, a Connoisseur's Collection*, Peter Winkler

Answer: 
I think it's pretty obvious.

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>  They discuss a meeting place on the phone and then talk about it in person.
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;)

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Alternatively,

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>  one sheriff reads his two suspects' names. The other sheriff says nothing and goes to arrest the culprit.
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I'm finding one small issue with mine (in the worst case scenario), so hopefully this will help someone else.

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>  One sheriff reads names **NOT** on his list ("I know it isn't \_\_\_\_) until he reads a name on the second sheriff's list. We know the first sheriff will have to say some name he knows it isn't that the second sheriff thinks it is, or the case is unsolvable.  
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> The second Sheriff now knows the culprit. The second sheriff can now begin the same process ("I know it isn't \_\_\_\_") until he reads a name on the first sheriff's list. He needs to stop before the final name though if he gets that far, or he could still reveal who the culprit is (if the two sheriff's have together said it isn't 7 of the 8).
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I realize this isn't fullproof, given the situation of: 

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>  If luck is really bad and the second sheriff reads the entire list and the two remaining names (the culprit, and last person unsaid to avoid giving too much away) are both suspects to the first sheriff. Then this way wouldn't work.
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