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

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.

Another one:

Five runners - A, B, C, D and E took part in a race.There were 3 medals - gold, silver and bronze up for grabs.

A betting house took bets for each of the following five outcomes.

1) A won't win gold, B won't win silver.
2) C will win a medal, and D will not.
3) D and E will both win medals.
4) D will not win silver, E will not win bronze.
5) A will win a medal, and C will not.

All the people bet on any of the above five outcomes lost their money.

Who won the gold, silver and bronze medals?

Slack
I also made the same mistake. I thought 1 goat=1 chicken+ 1 dog.
However, I don't think the question was phrased wrong. It just wasn't phrased optimally.

1 goat=1 chicken + 1 dog, only when the dog never belonged to Rambo. He clearly said, he will give Shyambo ONE OF HIS DOG. If he is giving one of his dog, then that dog has to be subtracted from his account.

Let's move on.

Republican, how do you prove the triangle question?


Runners?
A=Gold
D=Silver
C=Bronze
And D & E got Aalu.

The triangle question:

IF you look at the first image, the slope of the main triangle is not actually a straight line, though very close to one. Because the slope of the two smaller triangles are not the same. You can tell by the ratio of their perpendicular and base sides - 2:5 and 3:8. The slope of the red triangle (with sides 3 and 8 units) is slightly less than the smaller one (with sides 2 and 5).

So in the first image, the straight line is actually bending inwards, taking up the space of that single square you see in the 2nd picture.

In the 2nd picture, when the smaller triangles are switched, the line is bending outwards, freeing up space for that single square unit.

Swatantra, how can D win silver and get Aalu as well : )

Anyway, care to explain your answer?

One of the night club required a "password" to get in ...one smart a$$ thought to give a try even if he didn't has the password...he decided to get a hint from other person entering with the password

The security: 12
first person: 6
he was let in
the security: 6
second person:3 !
het got in too

He thought he is prepared now
security (this time): 10

what should he answer as password that will put him through too ???

PS:if it was that easy, i wouldn't have asked it...you know it right?

spiral or circles???

both...depends how you look at it

Republican..
is the medal question...enough???? it looks like there are 2-3 possibilities..i may be wrong though.

born to rule: the answer is 3.

twelve = 6 letters

six = 3 letters

ten = 3 letters



Aashish: that's the question as it is.