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03 Jun 2022, 01:30
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Difficulty:
75%
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50% (02:32) correct
50%
(02:57)
wrong
based on 30
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In a magical swamp there are two species of talking amphibians: toads, whose statements are always true, and frogs, whose statements are always false. Four amphibians, Brian, Chris, LeRoy, and Mike live together in this swamp, and they make the following statements.
Brian: "Mike and I are different species."
Chris: "LeRoy is a frog."
LeRoy: "Chris is a frog."
Mike: "Of the four of us, at least two are toads."
How many of these amphibians are frogs?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Are You Up For the Challenge: 700 Level Questions
Brian: "Mike and I are different species."
Chris: "LeRoy is a frog."
LeRoy: "Chris is a frog."
Mike: "Of the four of us, at least two are toads."
How many of these amphibians are frogs?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Are You Up For the Challenge: 700 Level Questions
03 Jun 2022, 03:38
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If Brian is lying, then Mike is lying too, however his statement of there being at least two toads amongst the four would then mean that the actual truth is that there is only a single toad which cannot hold if they are both toads. Thus Brian is telling the truth, which means that Mike is lying, so as there is only 1 toad then both Chris and LeRoy are telling the truth.
1 lying toad.
3 truthful frogs.
Answer C
1 lying toad.
3 truthful frogs.
Answer C
03 Jun 2022, 05:07
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Assume Brian is a frog and is therefore lying.
That would mean Mike is also a frog, which then suggests an examination of Mike's statement, which is a lie under this scenario.
For Mike's statement to be a lie, there are either 4 frogs/0 toads or 3 frogs/1 toad.
Can there be 4 frogs ? That would mean Chris and Leroy's statements would have to be false.
For Chris's statement to be false means that Leroy is a toad, so there can't be 4 frogs.
Can there be 3 frogs ? Continuing from above, if Leroy is indeed a toad, then his statement that Chris is a frog is true.
Well, that is consistent with our assumption above.
So Brian, Mike and Chris can be frogs and Leroy a toad.
Answer D
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That would mean Mike is also a frog, which then suggests an examination of Mike's statement, which is a lie under this scenario.
For Mike's statement to be a lie, there are either 4 frogs/0 toads or 3 frogs/1 toad.
Can there be 4 frogs ? That would mean Chris and Leroy's statements would have to be false.
For Chris's statement to be false means that Leroy is a toad, so there can't be 4 frogs.
Can there be 3 frogs ? Continuing from above, if Leroy is indeed a toad, then his statement that Chris is a frog is true.
Well, that is consistent with our assumption above.
So Brian, Mike and Chris can be frogs and Leroy a toad.
Answer D
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