Sunday, 16 December 2012

Cards in a Square Puzzle - Solution


The Puzzle:

Take from a pack of cards all the Aces, Kings, Queens and Jacks.

Arrange them in a 4 × 4 square so that every row, column and diagonal contains one card of each value (A,J,Q,K) and one card of each suit (Heart, Spade, Diamond, Club).




Our Solution:

Here is one solution of many:


                 

Crates of Fruit - Solution

The Puzzle: You are on an island and there are three crates of fruit that have washed up in front of you. One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges.

Each crate is labeled. One reads "apples", one reads "oranges", and one reads "apples and oranges". You know that NONE of the crates have been labeled correctly - they are all wrong.

If you can only take out and look at just one of the pieces of fruit from just one of the crates, how can you label ALL of the crates correctly?


The Solution . . .

Take a piece of fruit from the "apples and oranges" crate. If it's an apple then you know that is the "apples" crate since ALL THE CRATES ARE LABELED INCORRECTLY. This means the crate marked "apples" must be "oranges" and the crate marked "oranges" must be "apples and oranges".

Breaking Up a Chocolate Bar - Solution

The Puzzle: How many steps are required to break an m x n bar of chocolate into 1 x 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).

The Solution . . .

You need mn – 1 steps.

By breaking an existing piece horizontally or vertically, you merely increase the total number of pieces by one.

You already have 1 piece, so need mn – 1 steps to get to mn pieces.

Burning Island - Solution

The Puzzle: 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)

The Solution . . .

The man picks up a piece of wood and lights it from the fire on the west end of the island.

He then quickly carries it near the east end of he island and starts a new fire. The wind will cause that fire to burn out the eastern end and he can then shelter in the burnt area.

The man survives the fire, but dies of starvation, with all the food in the forest burnt.