2011 CEMC Gauss (Grade 7) Problems/Problem 10

Problem

I bought a new plant for my garden. Anika said it was a red rose, Bill said it was a purple daisy, and Cathy said it was a red dahlia. Each person was correct in stating either the colour or the type of plant. What was the plant that I bought?

Solution 1

From what Anika said and the rules of the problem, we can conclude that the plant is red but not a rose or is not red but is a rose. Let's first assume that the plant is not red but is also a rose.

However, Cathy said that the plant was a red dahlia. This means that the plant is red but not a dahlia or is not red but is a dahlia. If the latter is true, we have a contradiction because the plant cannot be a dahlia and a rose at the same time. If the former is true, we also have a contradiction because the plant was already stated not to be red. Thus, the plant is red but not a rose, and we also know that it is not a dahlia from what Cathy said.

From what Billy said, we can conclude that the plant was either purple but not a daisy or was not purple but was a daisy. However, we know that the plant was not purple, so the former cannot be true and the latter conclusion must be true. This tells us that the plant must be a daisy.

From what we have concluded, the plant must be a .

~anabel.disher

Solution 2 (answer choices)

We can follow the same steps as solution 1 until we get to the point where we conclude that the plant is not a dahlia from what Cathy said. Since the plant is red, we know that C and E are the only possible answer choices. However, we also know that the plant cannot be a dahlia, so C is not the correct answer.

Because all of the other answer choices have been eliminated, the answer is .

~anabel.disher