Splitting Problem

How do you cut a rectangular cake into two equal pieces with one straight cut when someone has already removed a rectangular piece from it? (The removed piece can be of any size or any orientation.)

consider these images:

An Ant and a Cube

An ant starts eating a 3*3 rubik's cube made up of cheese at a corner(vertex). What is the probability that the last cube it eats is the body-center cube?


The ant can only travel from a cube to the adjacent cubes (i.e. having common faces)



Courtesy: Nitin Basant

Monty Hall problem a.k.a. The 3 door problem

Although I'm sure most of the ToughNut readers are familiar with this problem but I've met a lot of people with great aptitude who seem to have all sorts of confusion and disagree with the solution. Lets discuss and debate about the conflicting opinions that we all have. Here it goes...

Monty Hall problem

----------------------------------------------------------------------------------------------

Suppose you're on a game show and you're given the choice of three doors. Behind one door is a car; behind the others, goats. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice? 

5 Pirates Puzzle

Perhaps the most common of all math/logic puzzles being discussed in forums on the internet, yet an interesting one. Here it goes...

There are five rational pirates, A, B, C, D and E. They find 100 gold coins. They must decide how to distribute them.

The Pirates have a strict order of seniority: A is superior to B, who is superior to C, who is superior to D, who is superior to E.

The Pirate world's rules of distribution are thus: that the most senior pirate should propose a distribution of coins. The pirates, including the proposer, then vote on whether to accept this distribution. If the proposed allocation is approved by a majority or a tie vote, it happens. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again.

Pirates base their decisions on three factors. First of all, each pirate wants to survive. Secondly, each pirate wants to maximize the number of gold coins he receives. Thirdly, each pirate would prefer to throw another overboard, if all other results would otherwise be equal

Source:  Stewart, Ian (1999-05), "A Puzzle for Pirates", Scientific American: 98–99

Information for puzzle solvers!!

Hi puzzlers,

The very idea of ToughNut is to bring in as many challenging and brainteasing puzzles as possible and share them with the followers of this blog. To take the idea a step ahead I invite you all to participate in collaborative publishing. I encourage you to email puzzles directly to itsfreddo.toughnut@blogger.com and have them published on this blog. I would strongly encourage all contributors to mention their names in the end of the email so that they are fairly credited for their contribution to the blog.

I cannot guarantee that every puzzle sent to this email id shall be published. However, the puzzles fairly suiting the interests of the niche community of readers that this blog has shall definitely be published.

Warm regards,

Ankit

The Scared Guards Problem

561 security guards are positioned so that no two pairs of guards are the same distance apart. Every guard watches the guard closest to him. Is there an arrangement of the guards so that every guard is being watched?

Source: http://www.cs.rpi.edu/~magdon/miscellaneous/puzzles/puzzles.html