Logic Puzzles

04 Oct 2018

Introduction

This is a collected set of logic puzzles I have remembered and recorded. I have encountered most of these puzzles in my day to day life and thus do not know the true source for them. As of yet, none of these are my own original creations. If you know of any interesting logic puzzles that are of a similar format to those listed here please share them in the comments below (comments are a work in progress).

The Warden’s Chalice

There 100 prisoners in a high-security, solitary confinement prison. One day the warden releases all the prisoners from their cells into the central annex.

I have decided to give you all a second chance at freedom, but I need you to prove to me that you have the ability to work together as we all must do in a civilized society. If you can successfully complete the challenge you will all be set free, if you fail you will remain in solitary confinement until you serve out the rest of your sentences.

The warden points to the chalice on the table beside him and continues,

After I am done explaining the challenge you will have as much time as you wish to discuss amongst yourselves and form a plan in this central annex. Afterwards you will each be sent back to your cells and will not be allowed to communicate with each other except through this chalice. I will call prisoners out one at a time to this central annex. When you come out you will be allowed to perform one of the following three actions:

1. Flip this chalice from either the upright position to upside down or vice-versa,
2. Do nothing and return to your cell,
3. Or claim that every prisoner has been out to visit me at least once. To successfully win the challenge and gain freedom for you all a prisoner must correctly claim that every prisoner has been out to visit at least once. If one of your number incorrectly makes this claim then you will all fail and serve out the remainder of your sentences. I can call out the prisoners in any order I so choose. I may call out the same prisoner 100 times before I call out another. The chalice will start in the upright position. You may now discuss and come up with a plan before I send you all back to your cells.

How can the prisoners successfully complete the challenge with 100% certainty?

Blue Eyes Exile

On a remote island in the middle of the Atlantic a tyrant king rules. One day he decrees that all those on his island with blue eyes must leave silently in the middle of the night as soon as they know they have blue eyes and there is at least one islander who has blue eyes. If you are caught telling another islander the color of his eyes you will be executed immediately.

Now this island is quite primitive so there are no reflective surfaces anywhere. The water surrounding the island is too murky for an islander to see the color of his/her own eyes. In short, there is no way for an islander to directly observe their own eye color. Secondly, the population of this island is quite small so each islander greets and observes the eye color of all his/her neighbors on a daily basis. Thirdly, every islander is a perfect logician.

Given that there are exactly 7 islanders with blue eyes when will they all leave the island and in what order?

Gates to Heaven and Hell

You die and find yourself in a room with two doors and two angel guards. One of the doors leads to hell and one leads to heaven. One of the guards will always tell the truth and the other will always lie. The guards know which door leads to heaven and which door leads to hell, but you have no idea. You have the opportunity to ask one of the guards a single question to figure out which door you should enter. What question do you ask the guards?

Execution by Marbles

While traveling in a foreign land you are arrested by authorities for violating one of their obtuse laws. The punishment of course is death.

The king of this land however believes in redemption for those who are guileful and lucky. To this end he

Petals Around the Rose

The name of the game is Petals Around the Rose. I can tell you three things about the game: the score to every roll is either even or 0, the name which is important, and the score to any particular roll. Let me give you an example.

Pirates splitting up gold

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