I have three differently-colored stuffed animals: an ant, a bat, and a cat. One is obsidian, one is chartreuse, and one is phthalocyanine blue. Exactly one of these three statements is true:
The ant is obsidian.
The bat is not obsidian.
The cat is not phthalocyanine blue.
Tell the color of each animal.
Solution
We have to solve this problem in two steps. First, we have to figure out which one statement is true. If (a) is true, then (b) is also true, so (a) is not the one true statement. If (b) is true, then either the ant or the cat is obsidian, so either (a) or (c) is also true. Thus (b) is not the one true statement. Therefore, (c) is the only statement that can be true while the other two are false.
Since (b) is false, the bat is obsidian, so the cat must be chartreuse (not phthalocyanine blue or obsidian), and the ant is phthalocyanine blue.