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Suppose that X is the connected sum of g tori. Let Y be the connected sum of X with a projective plane. Then Y is

Suppose that X is the connected sum of g tori. Let Y be the connected sum of X with a projective plane. Then Y is nonorientable and therefore is the connected sum of n projective planes for some n. Calculate a formula for n in terms of g.

Write a proof of your formula.

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