Mathematicians' Casino
Puzzle 1: Lightbox
You stop in front of the Light Box with three silver dollars in your hand. The light box displays red, yellow and blue lights, one at a time, always in the following repeating order: You drop a dollar in the slot. The machine flashes lights too quickly for you to follow for a few seconds, then stops on red. A message appears on the monitor: If you correctly predict the next color, you will win $10. Here are two hints: - Either the next color is blue, or the 100th color after the color currently displayed will be blue.
- Either the previous color was blue, or the 100th color before the color currently displayed was blue.
What will the next color be?
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