A doctor in Michigan has a sister who lives in California but the sister does not have any brother that lives in Michigan, how come??
:P

Republican, I tried more than an hour finding it mathematically, but everytime I get dog = $0.

This is what I did. Please tell me where I am wrong, if I am.

1 cow's price = $x
i.e. c = x
Total number of cows = n
Also, x = n

Total cow's price = c * n = x * x = x^2

For goat,
1 goat = $10

In terms of price,

x^2 = 10g + chicken -------- (i)

According to given condition:

(Understand the equation in terms of price)

(X^2)/2 = [ (10g - g) / 2 ] + chicken + dog
(X^2)/2 = (10g - 10) / 2 + c + d ------- (ii)

From equation (i) and (ii),

10g + c = 5g - 5 + c + d;
Therefore, 10g + c = 5g - 5 + 10 (given, g = c + d = 10)



(10g + c) / 2 = 5g + 5
10g + c = 10g + 10
Therefore, c = 10;

Hence, dog's price = $0

Well, it works mathematically that chicken also cost $10...maybe the those two guys just bought the chicken to make us confuse!

Please tell me where I am wrong on the above solution!

Correction:

From equation (i) and (ii),

10g + c = 5g - 5 + c + d
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(10g + c) / 2

Therefore, 10g + c = 5g - 5 + 10 (given, g = c + d = 10)
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V

(10g + c) / 2

According to my logic when A gives dog from his side to B then A is losing the price of dog so I assumed the equation as

10 - d = c + d

d = (10 - c )/2 ------------------(i)

Lets start form beginning

Suppose price of a cow is x, then total price of cow is x^2. The price per goat is 10 and number of goat is odd. With x^2 sum we have to buy any odd number of goat.

For the quotient to be odd while dividing x^2 by 10, remainder always equals 6. Lets check it with these squared numbers.
25 = 2*10 + 5 (even number of goat)
36 = 3*10 + 6 (odd number of goat)
49 = 4*10 + 9 (even)
81 = 8*10 + 1 (enen)
196 = 19*10 + 6 (odd)
256 = 25*10 + 6 (odd)
625 = 62*10 + 5 (even)
676 = 67*10 + 6 (odd)

In each case money left after buying even number of goat is 6 which is not other than the money to buy one chicken.

Now according to the equation (i) above price of dog becomes 2.

Slowpoison wrote:

"According to my logic when A gives dog from his side to B then A is losing the price of dog."

I think that is incorrect. The question says, when one of them gets extra goat, and to make them equivalent in terms of money, one has to give one dog besides the chicken he already has.

So, it is 1 dog + 1 chicken = 1 goat

What do you say, slowpoison? And, Republican, it's time to give the answer! :)

slowpoison, your solution is correct. Very nice!

slackdemic, sorry if you interpreted the question differently.

the equation would be:

1 goat - 1 dog = 1 chicken + 1 dog

I object, Republican! :P

Not meaning to fight with you, but I will post later why I disagree. In the class now.

Later!

Rambo says to Shyambo - I'll take the last goat, you can have the chicken.

Shyambo says - No way! A chicken costs less than a goat!

Rambo says - I'll also give you one of my dogs and we will be even.

Shyambo agrees.

How much does a dog cost?

The question clearly states that to make even Rambo gives one dog.

So, it clearly implies 1 goat = chicken + dog.

The question wasn't phrased clearly.

To begin with, the statement:
"They sell all their cows - each cow gets sold for an amount that is equal to the total number of cows they had, .."
is little ambiguous.

If you read that carefully, then the total amount you get from selling all cows will NOT be x^2. It will be (x^2 +x)/2.

And, this whole thing about
1 goat = 1 chicken + 2 dogs
does not make sense to me. It would be so only if the dog was bought using the money that belonged to both of them. We simply do NOT know if that is the case.

Well, I didn't come up with that question. I came across it and interpreted and solved it the way slowpoison did. Apparently it is the correct answer. If you guys want to do it in a different way, you are more than welcome.

Try this:

Hehe getting more complex!!!!
I think if the dog was bought by the money that came from selling the cows then
1 Goat=1 Chicken+1 Dog will be correct
However case here is not so, the dog (money) was came from Rambo's personal pocket, so he is giving away money so,
1 Goat-1 Dog=1 Chicket+1 Dog will be true

Am I right?

Triangle? By moving parts, we are just making bigger triangle, it is little hard to see (Looks almost same to naked eyes) but one can see the difference in diagonal lines intersecting with graphs in two figures.

To begin with, the statement:
"They sell all their cows - each cow gets sold for an amount that is equal to the total number of cows they had, .."
is little ambiguous.

Why ambiguous? It just means, if they had 50 cows, 1 cow costs $50. And, how come total price x^2/2? It IS x^2.

"1 Goat=1 Chicken+1 Dog will be correct
However case here is not so, the dog (money) was came from Rambo's personal pocket, so he is giving away money so,
1 Goat-1 Dog=1 Chicket+1 Dog will be true "

Swatantra, we do not need to consider if the money was taken out of the pocket or whatever, they had to be even, because one goat was extra. And, we are NOT finiding the price of cow here. We simply need to know what dog worths.

And to make, what the question says even, one of them gives away the chicken AND dog, to make equivalent, in terms of money. So, why in the world it is not

goat = dog + chicken ?

Slackdemic ( Slacks+Academic=Slackdemic hehehe, joking ;-), now you got your own version of red caps problem hehehhhehe. I tried few times and also came up with chicken=$10, which is not true at all. Equation is just trying to balacne out because dog does not include in original amount and also if chicken's price is $10, they would have bought an another goat instead of this freaking chicken.
g-d=c+d is true as I understood as bellow:
Let say, you are Rambo and I am Shyambo. Our dad Mogambo gave a goat and a chicken to us and told to sell them in Saturday Hatia and split the money between us. Here we are off to market licking baraf ice cream. You went one side with the goat to sell and I went other side with the freaking chicken. You have sold the goat for $10 and I have sold the chicken for $6. Since our dad told us to split the money in half, I cried and demanded $2 (dog) from you. Am I making sense here? or just blah..blah...anyway seems like just you and I are the only two pumping the heart of this thread, where are others?

Swantatratagaamy (phew!)...You make sense.

"They sell all their cows - each cow gets sold for an amount that is equal to the total number of cows they had, .."

Here is how I interpreted the above sentence by which I got the total initial sum to be (x^2+x)/2.
Let's say they started with x cows. The first cow is sold at $x. Then they are left with (x-1) cows. The second cow is sold at $(x-1), and so on and on.

No of cows left Amount recieved
x x
x-1 x -1
x-2 x-2
x-3 x-3
. .
. .
. .
x - (x-2) x-(x-2)
x-(x-1) x- (x-1)

So, if you sum up the second column, you get (x^2+x)/2. May be I was reading in "too much" but that's the way I interpreted what that sentence meant.

Anyway, keep these coming!

The table got messed up.

No of cows left Amount recieved
x =========> x
x-1 ========> x -1
x-2 =========>x-2
x-3 =========> x-3
. ===========> .
. ===========> .
. ===========> .
x - (x-2) ========> x-(x-2)
x-(x-1) ==========> x- (x-1)

Each cow gets sold for an amount that is equal to the total number of cows they had,

i.e. price of a cow = number of cows they owned.
Guest4, it does not say COW THEY HAD LEFT, instead it says COWS THEY HAD, which I have interpreted as original number of cows and apply it for all cows. To my understanding it simply says if they had 6 cows, then they sold all cows for $6 each.

Swatantra, you got that ALMOST right, but still it means somewhat different than what you came up with. I mean my nick: Slackdemic. It is actually one of my very favorite words. It is a very young word that is not yet in dictionary. (And, I don't want to disclose its meaning now :P)

You wrote:
You have sold the goat for $10 and I have sold the chicken for $6. Since our dad told us to split the money in half, I cried and demanded $2 (dog) from you. Am I making sense here?

Yes, I understand what you are saying, but I still can't comprehend the details associated with it! Why would you only cry for $2.00? Well, if I give you a dog, in the case you mentioned, you still have $8 and $10 and the money that was raised by selling those cows were not evenly distributed.

I just think that the dog was given to make things even there...so that both of them would have EQUAL money.

Guest4, I agree, the question is confusing, but "each cow gets sold for an amount that is equal to the total number of cows they had" should mean all of the cows were sold to the total (=initial) numbers of the cow they had.

Now will it still make me a dumb, if I again say the total price is x^2? :)

"you still have $8 and $10"

to be read:

you still have $8 and I have $10.

Oh, Swatantra, I think we should get over with this puzzling puzzle and keep up with other puzzles, shall we? ;) :) :D

Haha red and white cap for you.
I have $6 (chicken) and you have $10(goat), once you gave me $ 2, we both have $8.
Got to go. good night.