Math Question: Story Problem

[bmacd]

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 Mile 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 four amphibians are frogs?

 

[TuxDave]

oh.. nvm, i see my error. It's 3.

 

[Seru Wolf]

I agree... This doesn't make sense to me.

 

[Freshgeardude]

42

 

[bmacd]

@TuxDave - what was the reasoning that led you to your conclusion?

 

[TuxDave]

@TuxDave - what was the reasoning that led you to your conclusion?

In a nutshell:

Either Chris or Leroy is a frog but not both.
Brian can't be a toad which makes Brian and Mike a frog.

That's 3.

 

[yuchai]

I agree with 3 frogs.

1. Based on Brian's statement, consider all 4 possible combinations of toads/frogs between Brian and Mike - you will find that logically, there are two combinations that work, and both result in Mike being a frog. So, we know that Mike has to be a frog

2. Given that Mike is a frog, his statement is false. There are only 0 or 1 toads in total.

3. Now, look at the statements between Chris and Leroy. Logically, you will find that they can't both be frogs or toads. Based on this, we know that there is at least 1 frog and 1 toad.

4. Given 2 and 3, we know it's only possible that there is 1 toad. So, there are 3 frogs.

 

[joesmoke]

how do we know the frogs didnt give false names?

 

[TuxDave]

how do we know the frogs didnt give false names?

What if bmacd is a frog? O_O

 

[palswim]

how do we know the frogs didnt give false names?

This man thinks outside the box!

 

[darkxshade]

@TuxDave - what was the reasoning that led you to your conclusion?

I licked all 4 of them and only 1 got me high. So only 1 can be a toad.

 

[tyler811]

I voted three

 

[JujuFish]

Edit: Reverse the frog/toad. I misread the opening premise as frogs tell the truth and toads lie. So it should be 1 frog 3 toads.
Edit 2: No that doesn't work because Mike's statement screw that all up. Blah. Never mind Sucks misreading the OP.

 

[gimmewhitecastles]

how do we know the frogs didnt give false names?

The statements and names are made according to the narrator. For all intents and purposes, this guy must be telling the truth. If not, to hell with it all.

 

[mcurphy]

I don't think there is enough information to get a definite answer. It all depends on whether or not Brian is a Toad or Frog:

Brian: "Mike and I are different species"
If Brian is a Frog, this is false, and he and Mike are both Frogs.
Chris: "Leroy is a frog"
Leroy: "Chris is a frog"
One of these two HAS to be a toad and the other a Frog
Mike: "Of the four of us, at least two are toads"
If Brian is a Frog, then Mike is a Frog and this statement doesn’t matter.


Brian: "Mike and I are different species"
If Brian is a Toad, then Mike is a Frog.
Chris: "Leroy is a frog"
Leroy: "Chris is a frog"
One of these two HAS to be a toad and the other a Frog
Mike: "Of the four of us, at least two are toads"
If Brian is a Toad, then Mike is a Frog and this statement doesn’t matter.

So with this reasoning, the answer can be 2 or 3 Frogs.

Edit: Gah, nevermind. If you take into account that Mike has to be a Frog, no matter what Brian is, then Mike's statement has to be false. So there can't be Two Toads. So Mike must be a Frog, and thus the answer of 3 Frogs is correct.

 

[tyler811]

I don't think there is enough information to get a definite answer. It all depends on whether or not Brian is a Toad or Frog:

Brian: "Mike and I are different species"
If Brian is a Frog, this is false, and he and Mike are both Frogs.
Chris: "Leroy is a frog"
Leroy: "Chris is a frog"
One of these two HAS to be a toad and the other a Frog
Mike: "Of the four of us, at least two are toads"
If Brian is a Frog, then Mike is a Frog and this statement doesn’t matter.


Brian: "Mike and I are different species"
If Brian is a Toad, then Mike is a Frog.
Chris: "Leroy is a frog"
Leroy: "Chris is a frog"
One of these two HAS to be a toad and the other a Frog
Mike: "Of the four of us, at least two are toads"
If Brian is a Toad, then Mike is a Frog and this statement doesn’t matter.

So with this reasoning, the answer can be 2 or 3 Frogs.

Edit: Gah, nevermind. If you take into account that Mike has to be a Frog, no matter what Brian is, then Mike's statement has to be false. So there can't be Two Toads. So Mike must be a Frog, and thus the answer of 3 Frogs is correct.

I am glad I was not the only having a problem with this. For awhile there I thunking what moron i was beening