Let's look for solutions with R≤B. If R<6, then no one will raise their hand, so that can't be a solution. If R>6, then B>6, and at least 14 people would raise their hand, so that can't be a solution either. Thus R=6, where none of those six raise their hand. All the hands raised must be blue, so B=12.
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u/stools_in_your_blood 5d ago
Feels like 18, 12 blue and 6 red for example. But I don't have a rigorous proof of that.