"Simple" problems

1. ## "Simple" problems

The aim of the game: Write a deceptively simple question or problem.

The catch: A solution, or a link to further information, must be provided for the desperately curious.

What is 1? What is 2? What is 3? Define the natural numbers. Demonstrate that 2 + 2 = 4 using your definition.

2. Why is the sky blue?

3. Why is it that for natural numbers [1, 2, 3, ...] a, b, c and n, and for n greater than 2, are there no solutions for the equation an + bn = cn?

4. Is it true that every even number greater than 2 can be written as the sum of two primes?

5. Why are there no living animals as large as the dinosaurs?

6. What is the most straightforward way to define ignorance?

Spoiler tags don't work, so you might have to wait for the answer.

7. If a tree falls down and no one is there to hear it, does it make a sound?

8. But seriously, If a tree falls in the woods and no one is around to hear it, does it make a noise?

9. Here's a riddle for you: A girl is facetious. She is also abstemious. She gets pneumonia. Based on these clues, what American tree is she most like?

10. Those are not so much "simple" problems as they are out-of-the-box-thinking riddles...

Anyway.

Imagine you are on a game show. There are three doors. Behind one door is a goat. Behind another is a car. The other door has nothing behind it. You pick one. The host must open one of the two doors without a car behind it, and he does so. He offers you a chance to switch your choice to the other door.

Why do your chances of winning the car double when you switch?

11. Originally Posted by FabuVinny
But seriously, If a tree falls in the woods and no one is around to hear it, does it make a noise?

Hah???? Your just confusing me now. Sound is sound you can hear it.

What is the most spoken language in the world?

12. That's not a deceptively simple question.

No.

Yes, it is a very deceptively simple question. It really depends on your definition of 'language', and 'speak'. If by speak you include second, third, fourth, nth-language speakers, then, indeed, it's probably English. By first language speakers, depending on your definition of language, it's Chinese, or Mandarin.

13. Even if its the first language speakers English would win because if you put together all the English countries like UK, America, Australia, Canada- its more than the people who speaks Chinese or mandarin.

Whats π (Pie)=?

14. Whats π (Pie)=?

"Pie," as you've spelled it, is a dessert made with fruit. It's eaten best with ice cream.

"Pi," the number, is 3.14159265359...ad infinitum.

I have a question: what is the difference between a proof, a conjecture, and a lemma?

15. Originally Posted by Barb
Whats π (Pie)=?

"Pie," as you've spelled it, is a dessert made with fruit. It's eaten best with ice cream.

"Pi," the number, is 3.14159265359...ad infinitum.

I have a question: what is the difference between a proof, a conjecture, and a lemma?
A conjecture is a mathematical statement that is believed to be true, and has withstood substantial testing, but has not been proven. When proven, it becomes a theorem, which can then be used as a given in later work. A lemma is a theorem with little significance in and of itself, but which is useful in proving larger results. A proof is simply a set of statements which lead to the logical conclusion that a given statement must be true.

And pi, the ratio of the circumference of a circle to its diameter, is equal to 4*(1 - 1/3 + 1/5 - 1/7 + 1/9 - ...), among other formulas, and is approximately 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706 798214808651328230664709384...

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