Math brain teasers require computations to solve.
Achmed and Ali were 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 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 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.
What's the cost of a dog?
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.
Mar 08, 2002
|Come on, tell me what you think. I am of the opinion that the Comment box is way under used. If you like it great, If you hate it, tell me. So I can fix the problem in future puzzles. Personally I think more feedback both good and bad can only help the website produce more fun for all. Even a little trash talkin' can be fun.|
Mar 27, 2002
|umm..... ya... that's what i got too.... |
Mar 28, 2002
|I messed it up because I set it up that one sheep = 1 goat + 1 dog, not 1 sheep -1 dog = 1 dog + 1 goat.|
Jun 07, 2004
|I liked this teaser! I couldn't solve it because I misread the question but it was a good one anyway. |
Mar 07, 2006
|I made the 1 sheep=1 goat + 1 dog mistake too, but got the rest right. I thought it was a very thoughtful and well done teaser. I don't agree that the overall difficulty is as high as it's currently rated, but think it should be more popular than it's current rating also. Keep up the good work! |
Mar 03, 2009
|Awesome teaser! Really great! |
Properties of square numbers are practically a hobby for me, yet somehow that interesting fact had escaped. It was easy to deduce simply from the question being asked, but it was a great teaser.
I really like teasers where the question asked seems to come out of the blue and there doesn't seem to be enough information to answer it. Good job!
Apr 22, 2009
|I let the cost of a camel be x and therefore there are $x^2 available. If there are s sheep and a goat costs g then x^2 = 10s + g. But now a sheep ($10) equals a goat + 2 dogs 1.e. g = 10 - 2d. |
This gives us x^2 = 10(s+1) - 2d or 2d = 10(s+1) - x^2.
Since s is odd (can't be evenly split) we are looking for an even multiple of 10 minus the closest square number gives a result less than 10.
s = 1 gives d = 2 (trivial answer)
s = 3 gives d = 2. Up to 17 no answer < 10
s = 19 gives d = 2
At this stage it appeared from the pattern that there were many answers fro the number of sheep and cattle but always the same result for the dog.
Excellent teaser and I learned something new about square numbers!
Apr 22, 2009
Apr 08, 2017
|The scip model that I used to solve this teaser can be found at|
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