Logic Puzzles

11.

What costs a dog?

Achmed and Ali are camel-drivers, and on 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 is the same as the total of camels they owned. For that money, they bought as many sheep as possible at 10 dinars a sheep. For the money that was left, they bought a goat.
On their way home, they got in 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.

How much does a dog cost?

Submitted by tartle · Added 7 December 2007 · Updated 5 July 2026

Solution:

The goat costs 6 dinars, which is the price of a sheep minus the value of the dog. Since Ali took the last sheep, he owes Achmed a sheep's worth of value. Therefore, the dog must be valued at 4 dinars, making it equal in value to the difference between a sheep and a goat.


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Comments (4)

aatifahmed 22 December 2008

The dog costs 4 dinar.
The solution I am submitting below is encrypted so as not to take the fun out of your efforts! To decrypt use: www.rot-n.com
The cipher used is ROT18-ROT5 & ROT13.

Note that Ali and Achmed had equal number of camels (lets call n). Hence;
Total number of camels = 7n.
Total money they receive for camels = 9n^2
The sheep could not be distributed evenly among them, hence its an odd number (lets say 7m+1). And lets say that cost of one goat is g and one dog is d.
Therefore, 10*(7m+1)+g = 9n^2
Note g has to be even as the RHS is even. Also note that g is the unit digit of LHS, whereas the RHS is a square, leaving g to be only 6 or 4 (since 2 and 8 can never be unit digit of a square number, and 0 is not possible).
Now,
7m + (10+g)/10 = n^2
Thus g has to divisible by 10, which leave g to be only 6.
Since g is 6 and the distribution is equal so d has to be 4!!

alexonfyre 22 December 2008

I don't think it ever said they have equal number of camels aatifahmed...though it works if they do...I am pretty sure it is still true if they aren't equal numbers, however.

ChibiHoshi 18 March 2011

interestingly enough, if you look at a table of perfect squares, those with the tens place as an odd number (the only way there could be odd sheep) are always followed by a 6 (cost of a goat)
16,36,196,256,576,676,1156,1296,1936, etc.
So sheep-goat = dog
10-6 is 4

schizomidget 15 November 2016

The question is easy, all you need to do is set up some equations. But yeah, what interested me was that all perfect squares with an odd tens digit ended with a six. I wondered why so, and started coming up with explanations and this is what I've got:

0^2=00
1^2=01
2^2=04
3^2=09
4^2=16 ~ Ends with 6
5^2=25
6^2=16 ~ Ends with 6
7^2=49
8^2=64
9^2=81

I realized that it's not so much of a deal, it's just that all basic perfect squares that had an odd tens digit also ended with a 6. It just happens to be that way. So I guess this explains why this applies to all other numbers that are similar, since all of them (such as 196, 256, and 576) are squares of numbers that have a ones digit of 4 or 6.

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