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We are given a set of names and a set of papers with names written on each side of the paper (not necessarily different ones and either side of the paper can be empty). Can we place the sheets on a table such that every name shows up? Show that this problem is NP-complete.

I have difficulty in finding out an NP-complete problem from which it can be reduced to this problem.

I tried to reduce vertex cover and set cover problems but i was not successful. I am not sure if i am heading in the right direction.

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This is SAT in disguise. Every name corresponds to a clause. Every paper corresponds to a variable. Each side of the paper corresponds to a possible truth assignment to the variable.

If this is unclear, I suggest working out an example.

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