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:

Side A = 3 Cannibals, 3 missionaries
Side B = 0 Cannibals, 0 missionaries

1 cannibal and 1 missionary goes in the boat
Side A = 2 Cannibals, 2 missionaries
Side B = 1 Cannibals, 1 missionaries

1 missionary returns back and 2 cannibals go there
Side A = 0 Cannibals, 3 missionaries
Side B = 3 Cannibals, 0 missionaries

1 cannibal returns and 2 missionaries go
Side A = 1 Cannibals, 1 missionaries
Side B = 2 Cannibals, 2 missionaries

1 missionary and 1 cannibal return and 2 missionaries go
Side A = 2 Cannibals, 0 missionaries
Side B = 1 Cannibals, 3 missionaries

One cannibal back, two cannibals go
Side A = 1 Cannibals, 0 missionaries
Side B = 2 Cannibals, 3 missionaries

One cannibal back, two cannibals go
Side A = 0 Cannibals, 0 missionaries
Side B = 3 Cannibals, 3 missionaries

Thus all have crossed successfully

Solution:

10 Bulbs

For this tricky puzzle, you must check how many light bulbs in the row are having an odd number of factors. The first one surely has odd number of factors, the second has even, four has odd. Thus the bulb four and one will remain lit. The bulbs that are going to remain lit are perfect squares as they have an odd number of factors - 1, 4, 9, 16.

Since there are 100 passes, you can go up to 10 times 10 i.e. the square of 10. There are 10 perfect squares available to you - one, two, three, four, five, six, seven, eight, nine and ten. They corresponds to the bulb number 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. All of them will remain lit and thus total ten bulbs will remain lit after 100 passes.

Solution:

This question is one of the most common interview question. The most common answer of the question is sixty which is completely wrong. The second most common answer of this interview question is 10 which is wrong as well.

What we have is
6 fishermen catches 6 fishes in 6 minutes

If you offer them 10 times as much as time, they will surely catch 10 times as much as fishes as well
Thus the same six fishermen will be able to catch 60 fishes in 60 minutes.

You can also thing this in the unitary method.

If six fishermen catches 6 fishes in 6 minutes
Then, one fisherman will catch one 1 fish in 6 minutes
Thus in sixty minutes, one fisherman will catch 10 fishes (10 times the time, ten times the fishes).

Thus the right answer is six.

Solution:

24 times is the most common answer however that is completely wrong. The right answer will be 22 times.

Let us prove it by some simple mathematics.
Assume that it takes T hours for the minute hand to complete T laps. The hour hand will complete T/12 Laps in the same time.

Consider the situation when the hour hand and the minute hand will overlap for the first time; the minute hand would have completed one lap extra than the hour hands.
Thus, T =T/12 + 1

Considering the above expression we know that the first overlap will take place after t = 12/11 hours i.e. 1:05 am.

Similarly, the second overlap will take place when the minute hand would have completed two more laps than the hour hand.

Considering there are X laps,
T = T/12 + X

Everyone knows that a day comprises of 24 hours. Putting that in the equation we get
24 = 24/12 + X
Solve it and you will get
X = 22

Hence both of the hands will overlap 22 times in 24 hours.

Let us give you with those exact timings as well.
The hands will overlap at 12:00, 1:05, 2:10, 3:15, 4:20, 5:25, 6:30, 7:35, 8:40, 9:45, and 10:50. Do consider the fact that there will be no 11:55. It becomes 12:00.