Puzzle : Set Timer without Clock?

You are a cook in a remote area with no clocks or other way of keeping time other than a four-minute and a seven-minute hourglass. On the stove is a pot of boiling water. Jill asks you to cook a nine-minute egg in exactly 9 minutes, and you know she is a perfectionist and can tell if you undercook or overcook the egg by even a few seconds. 

How can you cook the egg for exactly 9 minutes?

You should follow THIS process! 

Solution : Setting up Timer without Clock!

What was the challenge?

We can set up a timer of 9 minutes using 4 and 7 minutes hourglass. Below is the process-

1. Flip both the hourglasses and drop egg into the water. 

2. After 4 minutes, 4-minutes hourglass will run out. Flip and reset it. ( 4 minutes counted and 3 minutes countdown left in 7-minute hourglass).

3. After 3 minutes, the 7-minutes hourglass will run out while 1 minute countdown will be left in 4-minutes hourglass. ( So far 4 + 3 = 7 minutes counted ). 

Flip the 7-minutes hourglass thereby resetting it's timer.

4. After 1 minute, the 4-minutes hourglass will run out. ( 4 + 3 + 1 = 8 minutes counted). 

5. At this point of time there will be sand for 6 minutes countdown left in 7-minutes hourglass. Just flip it so that it count exactly 1 more minute.
   

Now, that's how 4 + 3 + 1 + 1 = 9 minutes are counted.

 

The Last Bean in the Pot

A pot contains 75 white beans and 150 black ones. Next to the pot is a large pile of black beans. 

A somewhat demented cook removes the beans from the pot, one at a time, according to the following strange rule: 

He removes two beans from the pot at random. If at least one of the beans is black, he places it on the bean-pile and drops the other bean, no matter what color, back in the pot. If both beans are white, on the other hand, he discards both of them and removes one black bean from the pile and drops it in the pot.
 
At each turn of this procedure, the pot has one less bean in it. Eventually, just one bean is left in the pot. What color is it?

And the color of last bean is...... 

The Color of Last Bean in the Pot

Little story behind the title!

There are 75 WHITE beans in the pot i.e. they are odd in numbers. Since, they are always taken out in pair, in the end there will be 1 WHITE bean left out.

At some point, when there are 3 bean are left in the pot then there has to be 2 BLACK and 1 WHITE beans in the pot. They can't be 1 BLACK and 2 WHITE beans as for that 73 WHITE beans need to be taken out which is not possible since WHITE are always taken in pair.

So if cook pick 2 BLACK beans (or BLACK & WHITE) at this point then anyhow BLACK and WHITE will be left in the pot. Now, when he pick this pair of BLACK and WHITE then he puts BLACK on the pile and drop WHITE back to the pot as per his rule.

Eventually, WHITE bean will be left in the pot.

Who Stole The Money?

A man placed a $100 dollar bill on his desk and left for work. When he returned back the money was gone. He has three suspects: the cook, the maid and the electrician.

The cook said he put the bill under a book on his desk to keep it safe. The man checked and it is no longer there.

The maid said she moved the bill to the inside of the book between page 1 and 2 while she was cleaning. Again, the man checked the book and there was nothing between page 1 and 2.

The electrician said he saw the bill sticking out of the book and he moved it between page 2 and 3 to keep it safe.

Who stole the money?

Know who is the thief? 

The Electrician Stole The Money

Who were other suspects?

The electrician must be lying. Since the man checked between page 1 and 2 the next pair of page must be 3 and 4 not 2 and 3. The page numbers 2 and 3 must be the part of single page. 

So how can electrician move it between page 2 and 3?