Math Is Fun Forum

At auction, my brother buys two slightly used Boeing 746's, with the idea of flying one of them around the world. Now, if you buy two of these planes, the auction house throws in a tiny island right on the equator.

Now, everyone knows that the circumference of the earth is 25,000 miles. But, sadly, neither of these planes, which have exactly the same range, can go 25,000 miles on a full tank of fuel.

Tommy does the math, however, and he figures out that if he flies one plane, and I fly the other plane as a refueling plane, I can give him some fuel and I can fly back to the little island

So, at some point, you're going to give me some fuel, you're going to turn back, and I'm going to continue on.

Exactly. We're both going to just make it. I'm going to give you some of my fuel, and with my remaining fuel, I just make it back to the island. And with your initial supply of fuel, plus what I give you from my plane, you continue on your journey, and sometime the next day, if we're lucky, you make it back to the same island.

Having gone all around the world.

Right. So the question is: What's the range of one of these 746's?

There are a few conditions that have to be met. For example, there's no wind, because that would add something complicated to the procedure. And, there's zero time to transfer the fuel and zero time to turn around. And one other thing: The earth isn't rotating for the 24 hours or so it takes to complete this whole thing

*Leave what you think is the right answer

RAY: This next puzzler is mathematical in nature. Imagine two numbers, such that their product is equal to their sum. I'll give you two numbers: 5 and 1 and 1/4. You add them, and you get 6 and 1/4. You multiply them, and you also get 6 and 1/4.

TOM: You do?

RAY: You do! Now, I'm going to put on one additional condition. Both numbers have to be the same. For example, let's take 3/7ths as the number. 3/7ths and 3/7ths add up to 6/7. But, unfortunately, they multiply to 9/49ths. But if it worked, then, well, that would be the kind of answer I'm looking for.

TOM: So you're looking for whole numbers as well as fractions?

RAY: Any number you can think of. Fractions, irrational numbers, you name it, we'll use it.

Is there such a number that if you multiply it by itself the product is equal to adding it to itself?

If so, what are those numbers?

Of course zeros are not allowed, because everybody knows zero plus zero is equal to zero times zero. Zero is disqualified.

*Leave what you think is the right answer here!

Here it is:

It used to be that, when we changed into or out of Daylight Savings Time, you had to manually change all the clocks and appliances in your house.

Now many of them are wired into sources that change them for us.  So, for example, you change your wall clock and your microwave clock, but your computer, your cell phone your cable TV clocks automatically show the newly changed time without you having to do anything.

There is, however, a certain clock in my house that is not wired into anything. In fact, it runs on a battery, and it reads correctly all the time without my having to change it every spring and fall at the time changes.

The question is, how does it do this?

And the hint is, I didn't have one of these when I lived in Kansas.

*If yout think you know the answer then leave it here!

RAY: This next puzzler is from my "ceiling light" series.

Imagine, if you will, that you have a long, long corridor that stretches out as far as the eye can see. In that corridor, attached to the ceiling are lights that are operated with a pull cord.

There are gazillions of them, as far as the eye can see. Let's say there are 20,000 lights in a row.

They're all off. Somebody comes along and pulls on each of the chains, turning on each one of the lights. Another person comes right behind, and pulls the chain on every second light.

TOM: Thereby turning off lights 2, 4, 6, 8 and so on.

RAY: Right. Now, a third person comes along and pulls the cord on every third light. That is, lights number 3, 6, 9, 12, 15, etcetera. Another person comes along and pulls the cord on lights number 4, 8, 12, 16 and so on. Of course, each person is turning on some lights and turning other lights off.

If there are 20,000 lights, at some point someone is going to come skipping along and pull every 20,000th chain.

When that happens, some lights will be on, and some will be off. Can you predict which ones will be on?

*Leave what you think the answer is here please!*

RAY: This puzzler is from the matchstick series. Imagine, if you will, that you have four matchsticks of equal length. From those, you can easily make a square.

At each of the vertices, there is a right angle, or a ninety-degree angle, so there are four right angles.

TOM: I'm with you!

RAY: Now, using those same four matchsticks, make not 4 but 16 ninety-degree angles.

You might say, "Can I use the third dimension?" You can use any dimension you want.

I should mention, you are not allowed to fold, bend, break staple, or mutilate the matches in any other way.

TOM: Can you use mirrors?

*Leave your response here! Please!
RAY: No, but that shows you're on the right track.

RAY: Last month, Tommy and I were driving home from the Annual Seat Cover Convention. We stopped for gas along the highway. While our tank was being filled, we went inside to buy ourselves some soft drinks. As we reached inside the fridge to grab our drinks the kid behind the counter-- you know, with the one with the six nose rings-- said, "That machine was on the blink yesterday, and everyone was complaining all day that their sodas weren't cold. So, before I put these sodas in this morning, I cranked that baby up! I turned the thermostat way down. Boy, those suckers ought to be real cold now! I won't get any complaints today, I bet."

Tommy opens his bottle and begins drinking the soda. But when I open my bottle, it was frozen solid. I complained.

What happened?

Note:  Please post what you think is correct here!