In a certain flower garden, each flower was either red, yellow, or blue, and all three colors were represented. A statistician once visited the garden and made the observation that whatever three flowers you picked, at least one of them was bound to be red. A second statistician visited the garden and made the observation that whatever three flowers you picked, at least one was bound to be yellow.
Two logic students heard about this and got into an argument. The first student said: “It, therefore, follows that whatever three flowers you pick, at least one is bound to be blue, doesn’t it?” The second student said: “Of course not!” Which student was right, and why?
Puzzle – The Flower Garden
Solution: The first student was right, and here is why.
- From the first statistician’s report it follows that there cannot be more than one yellow flower, because if there were two yellows, you could pick two yellows and one blue, thus having a group of three flowers that contained no red. This is contrary to the report that every group of three is bound to contain at least one red flower. Therefore there cannot be more than one yellow flower.
- Similarly, there cannot be more than one blue flower, because if there were two blues, you could pick two blue flowers and one yellow and again have a group of three that contained no red. And so from the first statistician’s report, it follows that there is at most one yellow flower and one blue.
- And it follows from the report of the second statistician that there is at most one red flower, for if there were two reds, you could pick two reds and one blue, thus obtaining a group of three that contained no yellow. It also follows from the second report that there cannot be more than one blue, although we have already deduced this from the first report.
- The upshot of all this is that there are only three flowers in the entire garden-one red, one yellow, and one blue! And so it is of course true that whatever three flowers you pick, one of them must be blue.