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They finally arrive at the simultaneous conclusion that all three have blue dots on their foreheads. After the bear tells them at least one of them has a blue dot, if only one had a blue dot, that person would immediately have known the color of her own dot upon seeing red dots on the foreheads of the other two. If two of the three had blue dots, one of those two would have soon figured out that her dot was blue when the other person with a blue dot didn't immediately proclaim her dot as blue. So finally, it dawns on each of the three that the color of her dot must be blue.
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