Solving the Math Teacher Dinner Puzzle: Find the Date!

[GuMdRop]

I Need Help Immediatly!

I am in 7th grade algebra and I DONT get this problem at all:

That 'Math Teacher Dinner' is in December, but I forgot which night, so I asked around. Alan said that the date was an odd number; Brenda claimed it was greater than 13. Carly declared it was not a perfect square, while Dara swore it was a perfect cube. Finally, Edward told me the date was less than one-fourth of his age, which I know to be 68. Yesturday I learned that only one of them had told the truth! What is the date of the dinner?

well i have tried SOO many different ways to figure this out and it is due tomorrow! if u get the answer PLEASE tell me with a good explanation!
~thanks~

 

[arildno]

I'll get you started:
Suppose Alan is right (the number is odd).
Then Brenda is lying, so the number is either 13 or less than 13 (Ok?)
But consider Edward's statement:
He's saying that the number is less than 17 (agreed?)
But if Alan is right, Brenda MUST be lying; but this means that Edwards statement is actually true!
This is a contradiction, since Edward should lie if Alan told the truth.

Since our original assumption was that Alan told the truth, we have now shown that this leads to a contradiction.
Hence, Alan is lying and the number is EVEN.

 

[Gokul43201]

Start by listing the sets of possible dates according to each person.

I'll do the first one, you do the others :

A (Alan) = {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31}
B =
C =
D =
E =

Now list the sets corresponding to each person lying.

~A = {2,4,6,8,...,26,28,30}
~B =
~C =
~D =
~E =

Now there are only 5 cases to consider.
One of them is (A) and (~B) and (~C) and (~D) and (~E). What are the others ?

Which of these gives you an answer ?

(PS : Or you can do it arildno's way.)

 

[GuMdRop]

I TOTALLY get what you are saying, and it has helped me a little so thank you. but i still odnt know how to get the answer! i am very confused right now!

 

[GuMdRop]

wut is a perfect square, and wut is a perfect cube?

 

[arildno]

OK, the next one:
Suppose Brenda is telling the truth (that is, number bigger than 13).
(We already know, since Alan lies, that our number is even)
Then, Carly must be lying, that is our number must be a perfect square.
(The only perfect number over 13 and below 31 is 28, right?)
So, let's if our date might be 28:
Dara swore that it should be a perfect cube; if it is 28, then she has been lying.
This supports the assumption that Brenda told the truth.
Edward is also lying if our date is 28, since he said it should be less than 17.

So, conclusion is ...(fill out)

 

[Gokul43201]

perfect squares are the numbers you get when you square (ie :multiply by itself) the natural numbers.

For example 1*1 = 1, 2*2 = 4, 3*3 = 9,...So 1,4,9, ... are called perfect squares.

Similarly 1, 8, 27,... are perfect cubes (since 1*1*1 = 1, and 2*2*2 = 8,... )

 

[GuMdRop]

huh...i don't get it

 

[Gokul43201]

OK, the next one:
Suppose Brenda is telling the truth (that is, number bigger than 13).
(We already know, since Alan lies, that our number is even)
Then, Carly must be lying, that is our number must be a perfect square.
(The only perfect number over 13 and below 31 is 28, right?)
So, let's if our date might be 28:
Dara swore that it should be a perfect cube; if it is 28, then she has been lying.
This supports the assumption that Brenda told the truth.
Edward is also lying if our date is 28, since he said it should be less than 17.

So, conclusion is ...(fill out)

arildno, percfect square...not perfect number.

 

[Gokul43201]

huh...i don't get it

Don't get what ?

 

[Motifs]

Don't get what ?

Please be nice to ladies!

 

[arildno]

arildno, percfect square...not perfect number.

UHUU! I go to bed, pull the blankets over my head and disappear..

 

[GuMdRop]

i don't get arildno's way of doing it...it is totally confusing me...sorry it is kind of hard to explain stuff to me

 

[Gokul43201]

GuMdRop, arildno's gone to bed now. Let's leave him be.

Try what I suggested the first time. It's pretty straightforward.

(arildno, if you have an objection to my approach, let me know. Remember, this is for the 7th grade)

 

[Gokul43201]

Please be nice to ladies!

GuMdRop, I'm sorry if I came across as rude. I didn't mean to.

I was not sure whether you were referring to arildno's post or mine.

 

[GuMdRop]

gokul43201: your approach is pretty strait forward...but i don't get how u get the answeri listed all of the possibilities for if everyone were lying and not lying..but now what do i do??

 

[Gokul43201]

Can you write down the sets, so I can see them, and help you from there. Also, I can correct you if you've made any mistakes.

 

[GuMdRop]

never mind i got the answer now