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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?

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 doggylove123456 Aug 29, 2006 i like this teaser very much! jacket Sep 01, 2006 Why couldn't it be 1 green and 3 blue plates? tsimkin Sep 01, 2006 Because they have enough for themselves and for the 4 sisters. jacket Sep 01, 2006 oh ok jacket Sep 01, 2006 I wrote a BASIC program and finally came up with the answer. ztodd Oct 21, 2006 I figured out first that they could have 4 plates of which 3 are blue so the probability would be 3/4 * 2/3 = 1/2. But then I figured that since they said "not quite" when asked about feeding two dozen people, that you were probably looking for a larger number. You can get all the possibilities by graphing or just making a table of xy points from the equations: y/x * (y-1)/(x-1) = 1/2 x < 24 where y=blue plates and x=total plates and see which points from x=2 (at least 2 plates) to x=23 will give a whole positive number for y. x=4 and x=21 are the only two for x < 24.

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