## Two different purposes

You have to look at me to say what I show you. I offer two different purposes but I am spelled the same and I am pronounced the same.

WATCH and WATCH (Watch the watch).

You have to look at me to say what I show you. I offer two different purposes but I am spelled the same and I am pronounced the same.

WATCH and WATCH (Watch the watch).

My best buddy always makes mistakes. But I would easily get rid of the mistakes. What Am I?

An eraser (on pencil).

I look taller when I am young. But as I get old, I become shorter and shorter. What Am I?

A candle.

There are several chickens and rabbits in a cage (with no other types of animals). There are 72 heads and 200 feet inside the cage. How many chickens are there, and how many rabbits?

There are 44 chickens and 28 rabbits in the cage.
Let c be the number of chickens, and r be the number of rabbits.
r + c = 72
4r + 2c = 200
To solve the equations, we multiply the first by two, then subtract the second.
2r + 2c = 144
2r = 56
r = 28
c = 44

I have four legs.
I live in Africa.
I am big and grey.
I live in the river.
What am I?

I am a hippo.

Samuel was out for a walk when it started to rain. He did not have an umbrella and he wasn't wearing a hat. His clothes were soaked, yet not a single hair on his head got wet. How could this happen?

He is bald.

It is impossible to keep it until you give it someone else. What is that?

A promise.

You are somewhere on Earth. You walk due south 1 mile, then due east 1 mile, then due north 1 mile. When you finish this 3-mile walk, you are back exactly where you started.
It turns out there are an infinite number of different points on earth where you might be. Can you describe them all?
It's important to note that this set of points should contain both an infinite number of different latitudes, and an infinite number of different longitudes (though the same latitudes and longitudes can be repeated multiple times); if it doesn't, you haven't thought of all the points.

One of the points is the North Pole. If you go south one mile, and then east one mile, you're still exactly one mile south of the North Pole, so you'll be back where you started when you go north one mile.
To think of the next set of points, imagine the latitude slighty north of the South Pole, where the length of the longitudinal line around the Earth is exactly one mile (put another way, imagine the latitude slightly north of the South Pole where if you were to walk due east one mile, you would end up exactly where you started). Any point exactly one mile north of this latitude is another one of the points you could be at, because you would walk south one mile, then walk east a mile around and end up where you started the eastward walk, and then walk back north one mile to your starting point. So this adds an infinite number of other points we could be at. However, we have not yet met the requirement that our set of points has an infinite number of different latitudes.
To meet this requirement and see the rest of the points you might be at, we just generalize the previous set of points. Imagine the latitude slightly north of the South Pole that is 1/2 mile in distance. Also imagine the latitudes in this area that are 1/3 miles in distance, 1/4 miles in distance, 1/5 miles, 1/6 miles, and so on. If you are at any of these latitudes and you walk exactly one mile east, you will end up exactly where you started. Thus, any point that is one mile north of ANY of these latitudes is another one of the points you might have started at, since you'll walk one mile south, then one mile east and end up where you started your eastward walk, and finally, one mile north back to where you started.

It can be cracked,
it can be made,
It can be told,
it can be played.
What is it?

A joke.

I am not alive but I grow. I don't have lungs but I need air. What am I?

Fire.