logic / lateral puzzles
For week 3, given the statistical nature of recent posts, here goes some logic and lateral puzzles.
Let's start with the easy ones:
1. You have two cups, one containing orange juice and one containing and equal amount of lemonade. One teaspoon of the orange juice is taken and mixed with the lemonade. Then a teaspoon of this mixture is mixed back into the orange juice. Is there more lemonade in the orange juice or more orange juice in the lemonade?
2. You have three boxes of fruit. One contains just apples, one contains just oranges, and one contains a mixture of both. Each box is labeled - one says "apples," one says "oranges," and one says "apples and oranges." However, it is known that none of the boxes are labeled correctly. How can you label the boxes correctly if you are only allowed to take and look at just one piece of fruit from just one of the boxes?
(My guess is males could have some trouble with this one, but I'm not certain):
3. At a family reunion were the following people: one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law, and one daughter-in-law. But not as many people attended as it sounds. How many were there, and who were they?
And let's get tougher!
4. You have two slow-burning fuses, each of which will burn up in exactly one hour. They are not necessarily of the same length and width as each other, nor even necessarily of uniform width, so you can't measure a half hour by noting when one fuse is half burned. Using these two fuses, how can you measure 45 minutes?
5. Three men, members of a safari, are captured by cannibals in the jungle. The men are given one chance to escape with their lives. The men are lined up and bound to stakes such that one man can see the backs of the other two, the middle man can see the back of the front man, and the front man can't see anybody. The men are shown five hats, three of which are black and two of which are white. Then the men are blindfolded, and one of the five hats is placed on each man's head. The remaining two hats are hidden away. The blindfolds are removed. The men are told that if just one of the men can guess what hat he's wearing, they may all go free. Time passes. Finally, the front man, who can't see anyone, correctly guesses the color of his hat. What color was it, and how did he guess correctly?
6. Of three men, one always tells the truth, one always tells lies, and one answers "yes" or "no" randomly. Each man knows which one each of the others are. You may ask three yes/no questions, each of which may only be answered by one of the three men, after which you must be able to identify which man is which. How can you do it?
7. You have ten boxes, each of which contains nine balls. The balls in one box each weigh 0.9 pounds; the balls in all the other boxes weigh exactly one pound each. You have an accurate scale in front of you, with which you can determine the exact weight, in pounds, of any given set of balls. How can you determine which of the ten boxes contains the lighter balls with only one weighing?
And the famous Monty Hall Paradox (will we have a debate here?) :
8. You are on a game show. You are shown three closed doors. A prize is hidden behind one, and the game show host knows where it is. You are asked to select a door. You do. Before you open it, the host opens one of the other doors, showing that it is empty, then asks you if you'd like to change your guess. Should you, should you not, or doesn't it matter?
