- Banned
- #1
ANSWER TO PREVIOUS MENTAL CHALLENGE
A SKATEBOARD SHORT OF A DOG
Paul and Ross have been cat-breeders of renown for many years. Their insight into the nuances of felines have won them much acclaim. However, they've always been allergic to cats and have finally decided that it is foolishness of the highest order to remain in the cat-breeding business.
They decide instead to venture boldly into dog-breeding. So they take all their cats to the local cat markets, and sell them off. In a coincidence surely worthy of any logic puzzle, the amount in dollars they receive for each cat is exactly the same as the number of cats they sold.
For this money they purchase as many dogs as possible at $10 a dog. And because they're a little bit zany, they spend the left-over money on a flea circus.
On their way home they have a massive fight about the merits or otherwise of swing music and decide to split up forever. Unfortunately, when they divide the dogs there is one dog left over. So Paul says to Ross "I'll claim the last dog and you can have the flea circus." "Hold your horses, Swing Boy," says Ross, "The flea circus costs less than a dog". "Ok", Paul says. "Then I'll give you one of my skateboards and we'll be even". And Ross agrees.
How much was the skateboard worth?
ANSWER: This question makes use of an interesting little fact of mathematics to give us the answer. We must note carefully the clues about the amount of money Paul and Ross spent.
First of all, we know that the money paid per cat and the number of cats was the same number. This means that the total amount of money Paul and Ross received for their cats was a perfect square. (i.e. Total Money = X Cats x $X = X2).
Secondly, due to the fact that Paul and Ross couldn't split the dogs evenly, we know there was an odd number of dogs.
Thirdly, because the dogs were $10 each, and there were an odd number of them, we know that in the amount of money Paul and Ross spent, the number in the tens place (or the second last digit in the number, if you like) must have been an odd number.
The interesting little fact of mathematics is that whenever a number is a perfect square and has an odd number in the second last digit, the last digit is ALWAYS a 6.
So even though we're not sure exactly what the amount of money was or how many dogs Paul and Ross bought, we DO know that the last digit of the money was $6 and that's what they spent on the flea circus. So Paul has an extra dog worth $10 and Ross has the flea circus worth $6. Paul gives Ross a skateboard and they call it even. Therefore, $10 - the value of the skateboard= $6 + the value of the skateboard. Therefore, the value of the skateboard is $2.
A SKATEBOARD SHORT OF A DOG
Paul and Ross have been cat-breeders of renown for many years. Their insight into the nuances of felines have won them much acclaim. However, they've always been allergic to cats and have finally decided that it is foolishness of the highest order to remain in the cat-breeding business.
They decide instead to venture boldly into dog-breeding. So they take all their cats to the local cat markets, and sell them off. In a coincidence surely worthy of any logic puzzle, the amount in dollars they receive for each cat is exactly the same as the number of cats they sold.
For this money they purchase as many dogs as possible at $10 a dog. And because they're a little bit zany, they spend the left-over money on a flea circus.
On their way home they have a massive fight about the merits or otherwise of swing music and decide to split up forever. Unfortunately, when they divide the dogs there is one dog left over. So Paul says to Ross "I'll claim the last dog and you can have the flea circus." "Hold your horses, Swing Boy," says Ross, "The flea circus costs less than a dog". "Ok", Paul says. "Then I'll give you one of my skateboards and we'll be even". And Ross agrees.
How much was the skateboard worth?
ANSWER: This question makes use of an interesting little fact of mathematics to give us the answer. We must note carefully the clues about the amount of money Paul and Ross spent.
First of all, we know that the money paid per cat and the number of cats was the same number. This means that the total amount of money Paul and Ross received for their cats was a perfect square. (i.e. Total Money = X Cats x $X = X2).
Secondly, due to the fact that Paul and Ross couldn't split the dogs evenly, we know there was an odd number of dogs.
Thirdly, because the dogs were $10 each, and there were an odd number of them, we know that in the amount of money Paul and Ross spent, the number in the tens place (or the second last digit in the number, if you like) must have been an odd number.
The interesting little fact of mathematics is that whenever a number is a perfect square and has an odd number in the second last digit, the last digit is ALWAYS a 6.
So even though we're not sure exactly what the amount of money was or how many dogs Paul and Ross bought, we DO know that the last digit of the money was $6 and that's what they spent on the flea circus. So Paul has an extra dog worth $10 and Ross has the flea circus worth $6. Paul gives Ross a skateboard and they call it even. Therefore, $10 - the value of the skateboard= $6 + the value of the skateboard. Therefore, the value of the skateboard is $2.
