Chapter 1.1: The World of Amphibia

The imaginary realm of Amphibia is home to talking frogs and toads, who often engage in discussions about themselves. Notably, toads are honest, while frogs consistently deceive. Your task is to identify which animals are frogs and which are toads based on their statements.

Problem 1: A claims, “Both B and I are frogs.”

Problem 2: C asserts, “At least one of D and I is a frog.”

Problem 3: E states, “Both G and H are toads.” G retorts, “That’s true!” while H counters, “No, that’s false.”

Problem 4: I and J engage in a conversation about themselves and K. I claims, “All three of us are frogs.” J insists, “Exactly one of us is a toad.”

Chapter 1.2: My Solutions to the Puzzles

To effectively solve the initial two problems, it’s helpful to consider both possibilities for each speaker—being a frog or a toad—and then analyze the logical outcomes that arise from those assumptions.

For instance, if A is a toad and always truthful, it would imply that both A and B are frogs, leading to a contradiction. Thus, A must be a frog, meaning A is lying, which indicates that B is actually a toad.

In a similar vein, if C were a frog, it would be lying, suggesting that both C and D are toads, which again results in a contradiction. Hence, C must be a toad, confirming that D is a frog.

For the last two problems, it's crucial to recognize the contradictory statements made:

In the interaction between G and H, their opposing claims reveal that they must be different types of animals. This implies that E is lying, thus E must be a frog. Consequently, since G agrees with E, G is also a frog, which means H must be a toad.

Regarding I, if I were a toad, it would create a contradiction, so I must be a frog. Since I and J contradict each other, it follows that J must be a toad. Given J's honesty, this means there can’t be any other toads, thus K must be a frog.

How well did you fare with these puzzles? I welcome your thoughts in the comments!