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The points $$(p + 1, 1), (2p + 1, 3)$$ and $$(2p + 2, 2p)$$ lie on the same straight line only if $$p =$$
-1 or 2
2 or 1
2 or $$\frac{-1}{2}$$
$$\frac{1}{2}$$ or 2
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