Riddles

M

Maverickinsky

Par 100 posts (V.I.P)
General Gasslefield, accused of high treason, is sentenced to death by the court-martial. He is allowed to make a final statement, after which he will be shot if the statement is false or will be hung if the statement is true. Gasslefield makes his final statement and is released.

The Riddle: What could he have said?

The Answer: General Gasslefield said: “I will be shot.” If this statement was true, he would have been hung and thus not be shot. But then his statement would be false, which implies that he should be shot, making the statement true again, etc… In other words: the verdict of the court-martial could not be executed and the general was released.
:tea:
 
I am a three digit number.
My tens digit is five more than my ones digit.
My hundreds digit is eight less than my tens digit.
What number am I?

The Answer: The Number 194.
 
Q: I run over fields and woods all day. Under the bed at night I sit not alone. My tongue hangs out, up and to the rear, awaiting to be filled in the morning. What am I?
A: A shoe.
 
Q: What can run but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps?
A: A river.
 
Q: I’m light as a feather, yet the strongest man can’t hold me for much more than a minute. What am I?
A: Breath.
 
Q: I’m the part of the bird that’s not in the sky. I can swim in the ocean and yet remain dry. What am I?
A: A shadow.
 
In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.

The Riddle : How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly?

The Answer: It is not possible to guess only three fruits correctly: the fourth fruit is then correct too! So nobody has guessed three fruits correctly and 123-43-39-31 = 10 people have guessed four fruits correctly.
 
An old farmer died and left 17 cows to his three sons. In his will, the farmer stated that his oldest son should get 1 / 2 , his middle son should get 1 / 3 , and his youngest son should get 1 / 9 of all the cows. The sons, who did not want to end up with half cows, sat for days trying to figure out how many cows each of them should get.

One day, their neighbour came by to see how they were doing after their father’s death. The three sons told him their problem. After thinking for a while, the neighbour said: “I’ll be right back!” He went away, and when he came back, the three sons could divide the cows according to their father’s will, and in such a way that each of them got a whole number of cows.

The Riddle: What was the neighbor’s solution?

The Answer: The neighbour borrowed an extra cow, to make the total number of cows 18. Then the oldest son got 1 / 2 of 18 is 9 cows, the middle son got 1 / 3 of 18 is 6 cows, and the youngest son got 1 / 9 of 18 is 2 cows. Since 9+6+2 = 17, the cows could be divided among the three brothers in such a way that the borrowed cow was left over, and could be returned to its owner.
 
You throw away the outside and cook the inside. Then you eat the outside and throw away the inside. What did you eat?

An ear of corn.

Alternate Solution

A chicken.
 
The man who invented it doesn't want it. The man who bought it doesn't need it. The man who needs it doesn't know it. What is it?
A coffin.
 
A solo dice game is played thusly: one each turn, a normal pair of dice is rolled. The score is calculated by taking the product, rather than the sum, of the two numbers shown on the dice.

On a particular game, the score for the second roll is five more than the score for the first; the score for the third roll is six less than that of the second; the score for the fourth roll is eleven more than that of the third; and the score for the fifth roll is eight less than that of the fourth. What was the score for each of these five throws?

10 is the score for the first roll.
15 is the score for the second roll.
9 is the score for the third roll.
20 is the score for the fourth roll.
12 is the score for the fifth roll.
 
A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

The only lockers that remain open are perfect squares (1, 4, 9, 16, etc) because they are the only numbers divisible by an odd number of whole numbers; every factor other than the number's square root is paired up with another. Thus, these lockers will be "changed" an odd number of times, which means they will be left open. All the other numbers are divisible by an even number of factors and will consequently end up closed.

So the number of open lockers is the number of perfect squares less than or equal to one thousand. These numbers are one squared, two squared, three squared, four squared, and so on, up to thirty one squared. (Thirty two squared is greater than one thousand, and therefore out of range.) So the answer is thirty one.
 
You must cut a birthday cake into exactly eight pieces, but you're only allowed to make three straight cuts, and you can't move pieces of the cake as you cut. How can you do it?

Use the first two cuts to cut an 'X' in the top of the cake. Now you have four pieces. Make the third cut horizontal, which will divide the four pieces into eight. Think of a two by two by two Rubik's cube. There's four pieces on the top tier and four more just underneath it
 
You want to hire a temporary employee for one month. You offer him reasonable wages, but the employee suggests an alternative. For the first day of work, he will be paid a penny. For the second day, two pennies. For the third day, four pennies. The salary for each subsequent day will be double the previous day's, until the one month term is over. Ignoring the legalities of such a situation, would it be a good idea to accept the potential employee's proposal?

Solution : Not at all. He'll earn $5,368,709.12 on the thirtieth day alone.
 
Two trains travel toward each other on the same track, beginning 100 miles apart. One train travels at 40 miles per hour; the other travels at 60 miles an hour. A bird starts flight at the same location as the faster train, flying at a speed of 90 miles per hour. When it reaches the slower train, it turns around, flying the other direction at the same speed. When it reaches the faster train again, it turns around -- and so on. When the trains collide, how far will the bird have flown?

Since the trains are 100 miles apart, and the trains are traveling toward each other at 40 and 60 mph, the trains will collide in one hour. The bird will have been flying for an hour at 90 miles per hour at that point, so the bird will have traveled 90 miles.
 
Two mathematicians, Albert and Isaac, chat. Isaac says he has three children who all have the same birthday (but who weren't necessarily born in the same year). Albert asks their ages. Isaac replies, "The product of the ages of my children is 72." Albert points out that this is not enough information to determine their ages. Isaac responds with another clue -- he tells Albert the sum of the ages of his children. But Albert again points out that there is not enough information. Finally Isaac says, "My youngest child is named Galileo." At last, Albert correctly determines the ages of Isaac's children. What are the ages?

Solution:
If the product of his three children's ages is 72, there are the following possibilities:

1 * 1 * 72 = 72
1 * 2 * 36 = 72
1 * 3 * 24 = 72
1 * 4 * 18 = 72
1 * 6 * 12 = 72
1 * 8 * 9 = 72
2 * 2 * 18 = 72
2 * 3 * 12 = 72
2 * 4 * 9 = 72
2 * 6 * 6 = 72
3 * 3 * 8 = 72
3 * 4 * 6 = 72
Isaac later gives Albert the sum of their ages, but we don't know what number he says. We do, however, know that Albert can't figure it out from that information. So, we take the possibilities listed above and add them up:

1 + 1 + 72 = 74
1 + 2 + 36 = 39
1 + 3 + 24 = 28
1 + 4 + 18 = 23
1 + 6 + 12 = 19
1 + 8 + 9 = 18
2 + 2 + 18 = 22
2 + 3 + 12 = 17
2 + 4 + 9 = 15
2 + 6 + 6 = 14
3 + 3 + 8 = 14
3 + 4 + 6 = 13
The only way Albert wouldn't be able to figure out Isaac children's ages by knowing the sum is if the sum was 14, because there are two possibilities. So either the children's ages are 2, 6, and 6, or 3, 3, and 8. But Isaac points out that he has a youngest child. So the ages must be 2, 6, and 6.
 
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