Who Murdered the King?

This is a riddle that I found. Read carefully!

The king lived in a round kingdom and he was extremely rich. But one day, he was murdered! There were three suspects at the scene of the crime: the baker, the gardener and the maiden. Here is what they said:

Baker: "I was too busy baking buns."

Gardener: "I was too busy gardening."

Maiden: "I was too busy cleaning the corners."

Who murdered the king?

My 'Archimedes Proof'

I attempted my own proof for Archimedes' Sphere and Cylinder. It shows how the volume of a sphere will have exactly 2/3 the volume of the smallest cylinder it can fit inside. My proof worked and I was really proud of myself (hahaha) and here it is.

The volume of a sphere=4/3 πr^3

The volume of a cylinder=πr^2 h

Cylinder r= Sphere r 2r=d (diameter)

From the diagram you can see that the diameter of the sphere will be equal to the h

eight of the cylinder (h=d), and as d=2r, by the transitive property, h=2r.

If we substitute 2r for h in the cylinder formula, we get:

Vc=πr^2 2r

To make it clearer, let's break it

 up:

Vc=π x r x r x 2 x r

If we rearrange it we get:

Vc=2πr^3 

To finish our proof let's add in the sphere formula:

4/3 πr^3/2πr^3 

We cancel out πr^3 from top and bottom:

 

4/3/2

Multiply by 3/3:

4/6

Reduce:

4/6=2/3

  2/3

  

  Ta da!

Not-so quick Brainteasers

1. Two trains are on the same track 300 km apart, facing each other. The train drivers, who have just finished their lunch, immediately leap into their trains and start speeding at each other (for unknown reasons). One train is driving at 92 km/h, the other is driving at 87 km/h. How long will it take for them to collide?

2. Two friends are going to take an eye exam. The first, named Ahmapook, takes her eye exam, while the second, Bahmapook, waits for his turn. In the end, he gets so bored that he takes out his camera and snaps a few pictures of himself. When it is his turn, Bahmapook accidentally knocks over a sign in front of him. He puts it back upright and goes in for his exam. When he comes out, the two friends go to the counter. They had exactly the same test and they did not buy anything. Yet Ahmapook's bill is $100, and Bahmapook's bill is $1000. Why? (Hint: Bahmapook did not do any damage to the sign he knocked over)

3. 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 ... = (I got this problem from a book called "Poincare's Prize")

4. If 32 frogs can eat 32 flies in 32 minutes, How many flies are needed to eat 128 flies in 2 hours 8 minutes?

Quick Brainteasers

1. Think of an animal that starts with the letter 'a' and ends in ' l '. (Hint: Its name has two words.)

2. Two people wearing gas masks slowly walk into a room filled with gas. They then lock themselves inside. They rip off their gas masks, even though the room is still filled with gas. Why would they do that?

3. Two people are wrestling in a wrestling match. One is big and strong, but the other is nimble. It seems that no one will win. So each person would deliver one punch to the other and the one who died was the loser. The nimble one punches the big one, to no effect. When the big one punches, his punches kill the nimble one. Yet the nimble one still wins. Why?

4. What is 1/2 of 2/3 of 3/4 of 4/5 of 5?

5. 19023648! x (sin56-cos34)=