think again!

There are many ways to teach that the angle of reflection equals the angle of incidence, or whatever the term is, but this must be one of the most entertaining.

- She was a magician. By looks and by profession.
- What do you mean?
- One day she took a pack of cards numbered from 1 and upwards and divided them into two piles.
- Unaided?
- Yes, and not only that. She did it in such a way that no two cards in a pile added to a square number.
- That’s what I call magic!
- How many cards were there in the pack?
- I don’t remember. Probably not too many.
- How many is ‘probably not too many’?

The ones who want to be writers read the reviews, the ones who want to write don’t have the time to read reviews. - William Faulkner

- Have you been to Egypt?
- Have I been to the moon? Do I like sardines? Am I going bald?
- What are you rambling about?!
- Of all the questions in the world, you picked the one I don’t know the answer to.
- What do you mean?
- The Egyptians used unit fractions. The number one was always in their numerator.  
- And?
- I met an Egyptian once and he asked me a question about Egyptian fractions.
- And?
- I don’t know if I was just dreaming or if I met him in Cairo. That is why I can’t answer your question.
- I see. No offence meant.
- No taken.
- What did he ask you?
- He was a strange guy. A farmer. Growing tomatoes along the Nile. He had studied in Alexandria. Once he …
- What was his problem?
- He wondered if 4/n could be written as the sum of just three Egyptian fractions. If it was he would grow his tomatoes differently.
- Let me see if I understand you.
- I have given up a long time ago, but be my guest.
- 4/5 = 1/2 + 1/4 + 1/20.
- That was fast!
- I looked at 4/5 as 80/100 and I knew that 80 can be written as the sum of factors of 100, 50 + 25 + 5.
- Ahem!?
- You know what, I think your friend was right. I think I can prove that 4/n can be written as the sum of just three Egyptian fractions!
- I didn’t say he was my friend.
- OK.
- By the way, he believed that there was only one way to do it. 4/5 = 1/2 + 1/4 + 1/20 and there is no other way to write 4/5 as the sum of three Egyptian fractions.
- That sounds very unlikely. I am sure he was wrong.
- Me too, but I can’t find a counter example.
- No problem. Give me a week and I will find one. 
- The tomato growers will thank you.

Reading made Don Quixote a gentleman. Believing what he read made him mad. - George Bernard Shaw

Imagine two ants, or an aunt and an uncle, sitting in opposite corners of a square. One of them would like to go to the other while the other just wants to sit still. The square measures 10 by 10 metres. 

There is a fence, with no thickness and varying height. The height of the fence at the corners is zero and its highest point is at the middle of the fence.  Actually, the height varies in such a way that if the ant goes straight to the wall, climbs it, descends on the other side, and goes straight to the opposite corner, it doesn’t matter which route the ant takes, they are all equally long.

It is hard enough to remember my opinions, without also remembering my reasons for them! - Friedrich Nietzsche

Which number is smaller: 420,000 or 420,399?

Hint

Language is the source of misunderstandings. - Antoine de Saint-Exupery

If you wonder if math questions have ever been asked on Jeopardy!, here is the answer.

One of the two questions above is mathematical. Decide which and try to answer it.