Logic Puzzle 4

Puzzle-1:

You have a basket containing ten apples. You have ten friends, who each desire an apple. You give each of your friend’s one apple.

Now all your friends have one apple each, yet there is an apple remaining in the basket.

How?

Puzzle-2:

You have three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble.

You pick a random bag and take out one marble.

It is a white marble.

What is the probability that the remaining marble from the same bag is also white?

Puzzle-3:

How many steps are required to break an m × n sized bar of chocolate into 1 × 1 pieces?

You can break an existing piece of chocolate horizontally or vertically.

You cannot break two or more pieces at once (so no cutting through stacks).

Puzzle-4:

A man is stranded on an island covered in forest.

One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process. 

There are cliffs around the island, so he cannot jump off.

How can the man survive the fire? (There are no buckets or any other means to put out the fire)

Puzzle-5:

You are at an unmarked intersection ... one way is the City of Lies and another way is the City of Truth. 

Citizens of the City of Lies always lie.

Citizens of the City of Truth always tell the truth.

A citizen of one of those cities (you don't know which) is at the intersection. What question could you ask to them to find the way to the City of Truth?