BrainDen.com - Brain Teasers
• 0

## Question

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?

## Recommended Posts

• 0

Sorry for the typos.

##### Share on other sites

• 0

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.

##### Share on other sites

• 0

Amazing! Thank you!!!

##### Share on other sites

• 0

question...

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

##### Share on other sites

• 0

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 by Molly Mae
##### Share on other sites

• 0

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 by heyozzy
##### Share on other sites

• 0

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.

##### Share on other sites

• 0

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".

##### Share on other sites

• 0

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 by heyozzy
##### Share on other sites

• 0

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 by witzar
##### Share on other sites

• 0

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

##### Share on other sites

• 0

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.

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.