[Guest]

One day, a teacher brings in some cupcakes. While his backed is turned, one (or more) of his students ate them. There are 5 students in the class and he is sure that those students whom have not eaten the cupcakes will tell him the truth and that the guilty students will tell lies. When the questioned the 5 students answer as follows:

Student 1: "One of us ate them"

Student 2: "Two of us ate them"

Student 3: "Three of us ate them"

Student 4: "Four of us ate them"

Student 5: "Five of us ate them"

How many of the students were honest?

[Guest]

Sorry for the typos.

[Molly Mae]

Student 4 is telling the truth. If three or fewer ate the cupcakes, you'll have a student who didn't eat cupcakes lying (which isn't possible per the OP). If all 5 ate cupcakes, Student 5 ate cupcakes and is telling the truth (also not possible). Five different stories means that at least 4 are lying and only Student 4 can be telling the truth.

[Guest]

Amazing! Thank you!!!

[Guest]

question...

if 2 people ate a cupcake and one says "one of us ate them" is that a lie?

[Molly Mae]

question...

if 2 people ate a cupcake and one says "one of us ate them" is that a lie?

I assumed that it is. While the kid isn't saying "Only one of us ate them", he also isn't saying "At least one of us ate them." If you don't make that assumption, there's no definite answer.*

*EDIT: In fact, there's no answer that works.

Edited October 6, 2011 by Molly Mae

[Guest]

Hold on a second Molly. Student 1 says "One of us ate them" . What if he didn't eat any? Couldn't he be telling the truth then and the rest lieing?

This is a homework question that my 13 yr old daughter has to answer in her school in Tokyo. There should be a correct answer. My head hurts.

Edited October 6, 2011 by heyozzy

[Guest]

Hold on a second Molly. Student 1 says "One of us ate them" . What if he didn't eat any? Couldn't he be telling the truth then and the rest lieing?

This is a homework question that my 13 yr old daughter has to answer in her school in Tokyo. There should be a correct answer. My head hurts.

Rest all lying means they all ate.

[Molly Mae]

Hold on a second Molly. Student 1 says "One of us ate them" . What if he didn't eat any? Couldn't he be telling the truth then and the rest lieing?

This is a homework question that my 13 yr old daughter has to answer in her school in Tokyo. There should be a correct answer. My head hurts.

If he was telling the truth, then only one other person ate cupcakes. How can students 2, 3, 4, and 5 have eaten cupcakes if only one ate cupcakes? Further, if any of 2, 3, 4, and 5 didn't eat cupcakes, we have two conflicting "truths".

[Guest]

OK now it makes sense to me. If I consider the eaters as liers and not get caught up in the actual story... its pretty easy. Thank you Molly Rae and Amiab!

Is there some way for me to indicate this as being answered or doesn't it matter?

Edited October 6, 2011 by heyozzy

[witzar]

Obviously, exactly one of the five statements is true (since at least one must be true and no two can be true at the same time).

The remaining four must be lies, so exactly four students are lying.

The lying students are those responsible for cupcakes disappearance.

Edited October 6, 2011 by witzar

[Molly Mae]

Thank you Molly Rae and Amiab!

Is there some way for me to indicate this as being answered or doesn't it matter?

Molly Rae's a new one. I think I'll keep it, thanks. =P I like the sound of it.

There is a way to make is solved by using a poll, but it's not used as much in this forum as it is in New Word Riddles

[bhramarraj]

Obviously, exactly one of the five statements is true (since at least one must be true and no two can be true at the same time).

The remaining four must be lies, so exactly four students are lying.

The lying students are those responsible for cupcakes disappearance.

I like this answer. Since number of students, who ate the cake, is different in the statement of each student, therefore only one statement can be true; and since only one statement is true and four are lies, so four lying students ate the cakes and one telling the truth did not eat. So obviously fourth student did not eat cake and he is telling the truth.