Question: Assuming P != NP, for each of the problems below, say whether it is solvable in polynomial time or whether it is NP-complete, and justify

Assuming P != NP, for each of the problems below, say whether it is solvable in polynomial time or whether it is NP-complete, and justify your answer. (That is, if you say that the problem is polynomial-time solvable, explain how it can be solved in polynomial time; and if you say that it is NP-complete, give a polymomial-time reduction from an NP-complete problem to it.)

Given n coins of two different denominations (values), that is some coins are worth x dollars and some are worth y dollars, decide if the coins can be partitioned into two parts that have the same monetary value.

Is the coin problem do-able in polynomial time? If so explain the algorithm. If not then show a polynomial-time reduction from an NP-complete problem to this problem, such as boolean satisfiability.

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