#2. How much is the goat worth?

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Answer: $2

First, the brothers could not have started with a number of cows that would sell for a dollar amount that is cleanly divisible by 10, or else they would have no money left over for the goat.

Also, the amount of money the brothers receive for selling the cows must be a perfect square because each cow is sold for as many dollars as the brothers have cows, the amount of money they receive will always be a number multiplied by itself.

And finally, the final number of animals must be even, we know the brothers must have an amount of money that allows them to buy an odd number of lambs. That way, once you add in the goat, you’ve got an even number.

If you plug any of the numbers in that work for the riddle, you will find that the goat must have cost $6 (the number in the ones place). If the goat cost $6, then the brother who receives it is owed half the difference of the cost of a lamb and the cost of the goat, or: 1/2 ($10 – $6) = $2. This is the answer to the riddle, the brother who gets the goat will always be owed $2.

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