Sheepish Camels Can Bark!

Given Data, 1 sheep - 1 dog = 1 goat + 1 dog.

1 sheep - 1 goat = 2 dogs

Therefore 1 Dog = (1 Sheep - 1 goat )/2

We also know that a sheep is 10 dinars cost.

Let us assume the no. of camels be 'n'. Therefore as per the given data, the rate per camel is also 'n'. Therefore the total amount should be n-Square.

We also know that the no. of sheep bought is an odd no. Therefore the perfect squares when divided by 10, gives a quotient of odd no. are 36, 196,256 etc... Therefore the remainder is 6 when these perfect square divided by 10. So the cost of goat should be 6 Dinar. As per the equation 1 Dog = (1 Sheep - 1 goat )/2 1 Dog = (10 - 6)/2 = 2 Dinar

1 SHEEP - 1 DOG = 1 GOAT + 1 DOG, 1 SHEEP = 1 GOAT + 2 DOG, SHEEP cost 10 DINARs , 10 = 1 GOAT + 2 DOGs, (1 GOAT + 2 DOGs = 10 , which mean 1 GOAT is more expensive than 1 DOG), GOAT > 5, 1 DOG = 2 dinars, 2 DOG = 4 dinars, goat = 6 dinars, i don't understand why the other solutions showing SQUARE ?

Its the first time i am posting solution in maths so there would be some problem in my explaining, any questions are welcomed. let no. camels = x therefore total cost of camels = x^2. Since cost of 1 sheep = 10 . Therefore the equation is x^2 = 10y + n where y is the no. of sheep and n is the cost of the goat. also since 1 sheep is left at the end we can deduce that y is an odd no. also n < 10. according to the info, dog = (sheep - goat)/2. since both ahmed and ali have animals of same amount, if ali has even price then the price of ahmed should also be even. for this the price of goat and dog should be even. any even perfect square has 6 or 4 at its unit place. therefore the price of goat could be 4 or 6 (as price of goat is less than 10). now dog's price, either (10 - 6)/ 2 or (10-4)/2. Now since the price of dog should be even, first case is correct hence price of dog is 2.

they fought to get the last sheep, so the sheeps must be odd. So I decided 19 sheeps. It came from 14 camels. 14 14 = 196 196 = (19 10)+6 for example, the goat = y so, 10 - x = y + x, 10 - x = 6 + x, 10 - 2x = 6, x = 2

Cost of 1 sheep = S, Cost of 1 dog = D, Cost of 1 Goat = G, cost of all the camels = N N( N squire). Here, (S - G) = 2D , or, (10 - G) = 2D. They could not divide the sheep equally,so number of sheep is odd.Let number of ship = 2K+1. There fore, G = N N - 10(2K+1) , and 0 < G < 10 (as D > 0), => G = 6 for all favorable values of N & K. Hence, D = 2.

I randomly tried with n^2 and started with 36 since you get an uneven sheep composition. Final equation would be:

Ali: 2 Sheeps -1 dog = 1sheep+1goat+1dog. 20 -x = 10+ 6 +x x =2

the answer is 2

How I counted it: the sheep costs 10, so let's say the dog costs 2. 10 - 2 = 8 Say that the goat cost 6 dinars - 6 + 2 = 8. Which meant they were even .(it was kinda a guess, to be honest - but then I'm not that good at maths)

The dog is two dinars

let 'x' be no of camels=price of each camel total earnings=x^2 dinars let total no sheep bought=y price of one sheep=10 dinars total money spent on sheep = 10y dinars price of goat=x^2-10y dinars now x^2-10y<10 y must be odd and so satisfying the above condition we get x=6 and y=3 price of one dog=(price of one sheep-price of one goat)/2=10-36+30/2=2 dinars

The only bone of contention in this problem is, how come a goat costs 6 dinars?

I hope this helps.

Let x take the values of 0, 10, 20, 30 and so on. Square all possible numbers in terms of x.

1. (x^2) = 10(2p) + 0, p = 0 or even

2. (x + 1)^2 = (x^2 + 2x + 1) = 10(2p) + 1

3. (x + 2)^2 = (x^2 + 4x + 4) = 10(2p) + 4

4. (x + 3)^2 = (x^2 + 6x + 9) = 10(2p) + 9

5. (x + 4)^2 = (x^2 + 8x + 16) = 10(2p + 1) + 6

6. (x + 5)^2 = (x^2 + 10x + 25) = 10(2p) + 5

7. (x + 6 )^2 = (x^2 + 12x + 36) = 10(2p + 1) + 6

8. (x + 7)^2 = (x^2 + 14x + 49) = 10(2p) + 9

9. (x + 8)^2 = (x^1 + 16x + 64) = 10(2p) + 4

10. (x + 9)^2 = (x^2 + 18x + 81) = 10(2p) + 1

Notice that I equated each expression into such to show the remainder when divided by 10. Considering the values of x, it is safe to conclude that p is either 0 or even.

It can also be concluded from the problem that the number of sheep is odd. Observe that only numbers in the form (x + 4)^2 and (x + 6)^2 would give an odd value (i.e. 2p + 1) when divided by 10 (amount of each sheep). Notice further that they would only give a remainder of 6. That gives the amount of a goat.

Simply we just have to find a perfect square bigger than 10 as a sheep costs 10 Dinar. Now our perfect square must have an odd in tenth place as it wont be divisible by 2.. go ahead and you will find 36. 3 sheeps cant be divided among 2 people.And left is 6 Dinar.now add dog both side of the equation and you will find 1sheep - 1 goat= 2 dogs
So 2 dogs = 4 and dog = 2 :)

1 sheep=2 dogs. Also the total cost of all camels has to end with 76,96,56...I.e. 24^2,14^2,16^2 etc...If this happens then only sheep can distributed unevenly. So, 10(sheep)=6(goat)+2dogs So,Dog=2