Solution:

Fill the 3 quart bucket (5 quart bucket has 0 quarts and 3 quart bucket has 3 quarts)

Pour it entirely in the 5 quart bucket (5 quart bucket has 3 quarts and 3 quart bucket has 0 quarts)

Fill the 3 quart bucket (5 quart bucket has 3 quarts and 3 quart bucket has 3 quarts)

Pour the contents to fill the 5 quart bucket (5 quart bucket has 5 quarts and 3 quart bucket has 1 quart)

Empty down the 5 quart bucket (5 quart bucket has 0 quarts and 3 quart bucket has 1 quart)

Pour the water from 1 quart bucket to 5 quart bucket (5 quart bucket has 1 quart and 3 quart bucket has 0 quart)

Fill the 3 quart bucket (5 quart bucket has 1 quart and 3 quart bucket has 3 quarts)

Pour the contents from 3 quart bucket to 5 quart bucket (5 quart bucket has 4 quarts and 3 quart bucket has 0 quarts)

We are done and it took us eight steps to measure exactly 4 quarts of water.

Solution:

If you are thinking of how to cut in such a way that you are able to make seven equal pieces, you are thinking in the wrong direction. You should give more stress on how to make the transaction with the worker.

You have to break the gold bar two times so you have the following sizes of the bar:

1/7 ---- Bar A
2/7 ---- Bar B
4/7 ---- Bar C

When the day 1 ends:
Give Bar A (You remain with Bar B and Bar C; Worker possess - Bar A)

When the day 2 ends:
Give Bar B and take the Bar A back (You remain with Bar A and Bar C; Worker possess - Bar B)

When the day 3 ends:
Give Bar A (You remain with Bar C; Worker possess - Bar A and Bar B)

When the day 4 ends:
Give Bar C and take back Bar A and Bar B (You remain with Bar A and Bar B; Worker possess - Bar C)

When the day 5 ends:
Give Bar A (You remain with Bar B; Worker possess - Bar A and Bar C)

When the day 6 ends:
Give Bar B and take back Bar A (You remain with Bar A; Worker possess - Bar B and Bar C)

When the day 7 ends:
Give Bar A (You remain with no bar; Worker possess - Bar A, Bar B and Bar C)

Thus by the end of seven days, you have taken care of everything.

Solution:

This puzzle is also known as Monty Hall Puzzle. If Michael choose the box on the table, the probability of finding the pearl inside will be 2/3.

Let us consider the same thing with more boxes. If Sarah placed 100 boxes on the table with one box that contains the pearl and Michael is allowed to pick random, 99 boxes will remain on the table. Now at least 98 boxes in the table will be empty. Sarah will remove these 98 boxes and now Michael will have to choose from the box on table or the box in his hand. If he chooses the box below, the probability of finding the pearl in the box will be 99/100.

Now you must be convinced why he should pick the box on the table.

Solution:

Seven

Dividing the horses in a group of five, we will have five different groups of horses. A race will be conducted separately for each group which will help us find the fastest three horses in every group. We have used five different races till now.

Now we can have a race among the winners from every race which will help us determine the fastest of them all. We have used the sixth race.

The second fastest horse can be the one who came second in the sixth race or the second fastest horse in the finals winners' first race.

If we look at the first case, the third fastest horse can be the third fastest horse in the sixth race or the second fastest horse in either the fastest or second fastest horse first race.
If we look at the other case, the third fastest horse may be the second fastest in the sixth race or the third fastest in the final winners' first race.

If you calculate our assumptions, we have five more horses to race (seventh race) and determine the second fastest and the third fastest horse.

Solution:

The most often answer is 0 which is completely wrong.

Let us begin like this. The 12 hours in a clock makes a total of 360 degrees. Thus one hour will equal to 30 degrees.

Now as per the question, the hour hand will directly be on 3 when the minute hand is at 12. After 15 minutes or after 1/4 of an hour i.e. at 3:15, the hour hand will be 1/4 * 30 degrees = 7.5 degrees away from the minute hand.