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It means when you eat before going out and drink your life away. Then you wake up the following day feeling constipated and really have to go poop. But you can not because all the alcohol got sucked in to the food that you ate the night before.
Maria: I ate so much food and took too many shots. I think that was a bad idea.

Joce: Why?!

Maria: Because... I feel that I have alcohol constipation.
by Kimdizzle September 04, 2012