Achmed and Ali were camel-drivers and one day they decided to quit their job. They wanted to become shepherds. So they went to the market and sold all their camels. The amount of money (dinars) they received for each camel was the same as the total number of camels they owned. With that money they bought as many sheep as possible at 10 dinars a sheep. With the money that was left they bought a goat.
On their way home they got into a fight and decided to split up. When they divided the sheep there was one sheep left. So, Ali said to Achmed, “I take the last sheep and you can get the goat.” “That’s not fair,” said Achmed, “a goat costs less than a sheep”. “OK,” Ali said, “then I will give you one of my dogs and then we are even”. And Achmed agreed.
What’s the cost of a dog?
Answer
1 sheep – 1 dog = 1 goat + 1 dog
1 sheep – 1 goat = 2 dogs
A sheep is 10 dinars, but what does a goat cost?
The money they received for their camels is a square. And the digit in the tens-place of this square is odd (total money / 10 dinars), because they could not divide the sheep equally.
Now the interesting thing is that all squares with an odd tens-place end with a 6. (16^2 = 256, 24^2 = 576). So, a goat must cost 6 dinars.
10 – 6 = 2 dogs
So, a dog costs 2 dinars.
