Theories, Problems, Solutions

Einstein's Logic Problem

Crazy Horse — Fri, 02 Sep 2005 17:19:42 -0400

Given:

(a) There are 5 houses in 5 different colors.
(b) In each house lives a person with a different nationality.
(c) These 5 people drink a certain drink, smoke a certain cigar and have a particular pet.
(d) None of the people have the same pet, smoke the same cigar nor drink the same drink.

From the following statements, determine who will Keep the Fish

1: The Brit lives in a red house.
2: The Swede keeps dogs as pets.
3: The Dane drinks tea.
4: The green house is on the left of the white house.
5: The green house owner drinks coffee.
6: The person who smokes Pall Mall rears birds.
7: The owner of the yellow house smokes Dunhill.
8: The man living in the house right in the centre drinks milk.
9: The Norwegian lives in the first house.
10: The man who smokes Blend lives next to the one who keeps cats.
11: The man who keeps horses lives next to the man who smokes Dunhill.
12: The owner who smokes Blue Master drinks beer.
13: The German smokes Prince.
14: The Norwegian lives next to the blue house.
15: The man who smokes Blend has a neighbor who drinks water.

Jelly Beans

Crazy Horse — Fri, 05 Aug 2005 09:00:00 -0400

You have a large glass jar filled with Jelly Belly jelly beans. Some are green, some are yellow, some pink, some blue, and some are orange. With your eyes closed, pick out 2 of a like color. How many do you have to grab to be sure you have 2 of the same?

War Games

Crazy Horse — Wed, 20 Jul 2005 16:37:29 -0400

Dictator a is planning to slaughter the people of province q and province q anticipates the attack. Dictator a can either attack by air or by sea. Province q can either prepare for an aerial defense or a defense againt an assault by sea. Both sides must choose either an all air or all sea strategy, and they can't divide their armed forces. Given:

* If Dictator a attacks by sea and q defends by sea, the probability of massive slaughter is 80%.
* If Dictator a attacks by sea and q defends by land, the probability of massive slaughter is 100%.
* If Dictator a attacks by land and q defends by land, the probability of massive slaughter is 60%.
* If Dictator a attacks by land and q defends by sea, the probability of massive slaughter is 100%.

What should the strategy of Dictator a be, assuming the goal is to slaughter as many people of Province q as possible? Assume the goal of Province q to be to minimize the probability of mass slaughter. What is the final probability of mass slaughter assuming both utilize an the best strategy?

Marbles

Crazy Horse — Fri, 15 Jul 2005 22:58:47 -0400

Suppose that you have two jars, one with 50 red marbles and the other containing 50 blue marbles. First, a jar is picked at random, and then a marble will be picked from the corresponding jar. Placing all of the marbles in the jars, how can you maximize the chances of a red marble being picked? What are the exact odds of getting a red marble using your scheme?

What day is it?

Crazy Horse — Wed, 06 Jul 2005 17:03:04 -0400

If yesterday was Wednesday's tomorrow and tomorrow is Sunday's yesterday, what day would today be?

Diamond Flush

Crazy Horse — Tue, 05 Jul 2005 18:08:30 -0400

A cardplayer is dealt a poker hand (five cards) from an ordinary playing deck with the standard 52 cards. Find the number x of ways the player could be dealt a diamond flush (five diamonds).

Pleased to Meet You

Crazy Horse — Tue, 05 Jul 2005 12:31:54 -0400

If seven people meet each other and each shakes hands only once with each of the other, how many handshakes will have taken place?

Beatles

Crazy Horse — Fri, 01 Jul 2005 23:24:25 -0400

The Beatles have a concert that starts in 17 minutes and they must all cross a bridge to get there. All four men begin on the same side of the bridge. It is nightfall, and there is only one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, must have the flashlight with them, and the flashlight must be walked back and forth. Each band member walks at a different speed. A pair must walk together at the rate of the slower man's pace:

*Ringo: - 1 minute crossing
*George: - 2 minutes crossing
*Paul:- 5 minutes crossing
*John: - 10 minutes crossing

Example: If Ringo and John go first, 10 minutes have elapsed when they get to the other side of the bridge. If John then returns with the flashlight, a total of 20 minutes have passed and they have missed the concert.

There are two known answers to this problem.

Fuzzy Logic

Crazy Horse — Wed, 29 Jun 2005 20:53:39 -0400

One approach to handling fuzzy logic data might be to design a computer using ternary logic so that data could be stored as "true", "false", and "unknown". If each ternary logic element is called a flit, how many flits are required to represent at least 256 different values?

(a) 4
(b) 5
(c) 6
(d) 7
(e) 8

Formal Validity

Crazy Horse — Wed, 29 Jun 2005 10:50:48 -0400

If I do my homework then I will get better grades.

I didn't do my homework.

Therefore, I'm not going to get better grades.

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Valid or Invalid?