Taller De Matematicas

MATHEMATICAL LOGIC EXERCISES

NAME: _______________________________ ANSWER THE FOLLOWING PROBLEMS. 1. The Most Intelligent Prince

DATE: _____________ GRADE: ________

2. 100 Gold Coins

A king wants his daughter to marry the smartest of 3 extremely intelligent young princes, and so the king's wise men devised an intelligence test. The princes are gathered into a room and seated, facingone another, and are shown 2 black hats and 3 white hats. They are blindfolded, and 1 hat is placed on each of their heads, with the remaining hats hidden in a different room. The king tells them that the first prince to deduce the color of his hat without removing it or looking at it will marry his daughter. A wrong guess will mean death. The blindfolds are then removed. You are one of theprinces. You see 2 white hats on the other prince's heads. After some time you realize that the other princes are unable to deduce the color of their hat, or are unwilling to guess. What color is your hat? Note: You know that your competitors are very intelligent and want nothing more than to marry the princess. You also know that the king is a man of his word, and he has said that the test is a fairtest of intelligence and bravery. Answer: ______________________________ _____________________________________

Five pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treacherous and selfish (especially the captain). The captain always proposes a distribution of the loot. All pirates vote on the proposal, and if half the crew or more go"Aye", the loot is divided as proposed, as no pirate would be willing to take on the captain without superior force on their side. If the captain fails to obtain support of at least half his crew (which includes himself), he faces a mutiny, and all pirates will turn against him and make him walk the plank. The pirates start over again with the next senior pirate as captain. What is the maximumnumber of coins the captain can keep without risking his life? Answer: ______________________________ _____________________________________

3. 1 Gold Coin

Perhaps the hoot awakened the philosophers. As soon as they looked at each other, all three began, simultaneously, to laugh. Then, one of them abruptly stopped laughing. Why? Answer: ___________________________________________________________________

5. The 100 Coins There are 10 sets of 10 coins. You know how much the coins should weigh. You know all the coins in one set of ten are exactly a hundredth of an ounce off, making the entire set of ten coins a tenth of an ounce off. You also know that all the other coins weight the correct amount. You are allowed to use an extremely accurate digital weighing machine only once. How doyou determine which set of 10 coins is faulty? Answer: ______________________________ _____________________________________ So if given the choice between two outcomes, in which they get the same amount of money, they'd choose the outcome where they get to see more of the other pirates die. How can the captain save his skin? Answer: ___________________________________________________________________ 4. The Greek Philosophers 6. The Monkey and the Coconut

The five pirates mentioned previously are joined by a sixth, then plunder a ship with only one gold coin. After venting some of their frustration by killing all on board the ship, they now need to divvy up the one coin. They are so angry, they now value in priority order: 1. Their lives 2. Getting money 3. Seeing other pirates die.One day three Greek philosophers settled under the shade of an olive tree, opened a bottle of Retsina, and began a lengthy discussion of the Fundamental Ontological Question: Why does anything exist? After a while, they began to ramble. Then, one by one, they fell asleep. While the men slept, three owls, one above each philosopher, completed their digestive process, dropped a present on each...