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## The Gardner Sisters II

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #32684 Fun: (2.59) Difficulty: (2.28) Category: Probability Submitted By: tsimkin

Gretchen and Henry invited the four Gardner sisters over to their house for an afternoon tea. Henry went to the cabinet to take out some plates (they have both blue and green plates in the cabinet), and the first two plates he took out were blue. "What are the odds?" asked Martina Gardner, the youngest.

Henry thought for a moment, and then replied, "Knowing how many plates of each color I have, the probability that I would pull out two blue ones is exactly 1/2!" Martina then asked if Henry could feed two dozen people if he used all of his plates. "Not quite," he replied.

She then told him how many plates he had. What number did she say?

### Hint

He has more than 6 plates, so he could feed everyone, but less than 24. There is only one number in the middle of these that would satisfy the "exactly half" requirement.
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