Riddles

You are given eight jelly doughnuts. The doughnuts all weigh the same amount except for one which is heavier. You have a balancing scale at your disposal. What's the minimum number of weighings required for you to pick out the heavy doughnut every time?

Two. Weigh three of the doughnuts against three others and leave the remaining two on the table. If the scales are even, the heavy doughnut is one of the two on the table -- weigh them to find out. If the scales are uneven, take the three doughnuts on the heavy end, weigh one of them against another, and leave the third on the table. If the scales are uneven, you've found the heavy one. If not, the heavy one is the one on the table.
 
Three men stay at a hotel for the night. The innkeeper charges thirty dollars per room per night. The men rent one room; each pays ten dollars. The bellhop leads the men to their room. Later, the innkeeper discovers he has overcharged the men and asks the bellhop to return five dollars to them. On the way upstairs, the bellhop realizes that five dollars can't be evenly split among three men, so he decides to keep two dollars for himself and return one dollar to each man.

At this point, the men have paid nine dollars each, totalling 27. The bellhop has two, which adds up to 29. Where did the thirtieth dollar go?

The mistake is in how the thirty dollars are accounted for. The two dollars that the bellhop has are part of the 27 the men have paid. A correct accounting of the money is that 27 dollars were paid and three dollars were not, totaling 30 dollars.
 
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?

The back man can see the hats worn by the two men in front of him. So, if both of those hats were white, he would know that the hat he wore was black. But, since he doesn't answer, he must see at least one black hat ahead of him.

After it becomes apparent to the middle man that the back man can't figure out what he's wearing, he knows that there is at least one black hat worn by himself and the front man. Knowing this, if the middle man saw a white hat in front of him, he'd know that his own hat was black, and could answer the question correctly. But, since he doesn't answer, he must see a black hat on the front man.

After it becomes apparent to the front man that neither of the men behind him can answer the question, he realizes the middle man saw a black hat in front of him. So he says, correctly, "My hat is black."
 
A man is looking at a photograph of someone. His friend asks who it is. The man replies, "Brothers and sisters, I have none. But that man's father is my father's son." Who was in the photograph?

His son.
 
You have a 12 liter jug, an 8 liter jug, and a 5 liter jug. None of the jugs have any markings on them. The 12 liter jug is full, and the other two are empty. How can you divide the 12 liters of water equally (i.e., so two of the jugs have exactly 6 liters of water in them, and the third is empty)?

Fill the 8 liter jug with the 12 liter jug, leaving 4 liters remaining. Fill the 5 liter jug with the 8 liter jug, leaving 3 liters remaining. Empty the 5 liter jug into the 12 liter jug. Now there are 9 liters in the 12 liter jug and 3 liters in the 8 liter jug. Pour the 3 liters from the 8 liter jug into the 5 liter jug. Now fill the 8 liter jug with water from the 12 liter jug, leaving 1 liter in the 12 liter jug. Fill the 5 liter jug (which already has 3 liters in it) from the 8 liter jug, leaving 6 liters in the 8 liter jug. Empty the 5 liter jug into the 12 liter jug. Now there are 6 liters in the 12 liter jug, 6 liters in the 8 liter jug, and the 5 liter jug is empty.
 
A gambler bet on a horse race, but the bookee wouldn't tell him the results of the race. The bookee gave clues as to how the five horses finished -- which may have included some ties -- and wouldn't pay the gambler off unless the gambler could determine how the five horses finished based on the following clues:

Penuche Fudge finished before Near Miss and after Whispered Promises.
Whispered Promises tied with Penuche Fudge if and only if Happy Go Lucky did not tie with Skipper's Gal.
Penuche Fudge finished as many places after Skipper's Gal as Skipper's Gal finished after Whispered Promises if and only if Whispered Promises finished before Near Miss.
The gambler thought for a moment, then answered correctly. How did the five horses finish the race?

Whispered Promises came in first. Skipper's Gal and Happy Go Lucky tied for second place. Penuche Fudge came in fourth. Near Miss came in fifth.
 
In a rectangular array of people, who will be taller: the tallest of the shortest people in each column, or the shortest of the tallest people in each row?

This is a tongue twister of an explanation, but bear with me.

The shortest of the tallest people in each row will be taller than, or the same height as, the tallest of the shortest people in each column. There are four cases. The first is that the shortest of the tallest and the tallest of the shortest are the same person, so obviously in this case the shortest of the tallest and the tallest of the shortest would be the same height.

The second case is that the shortest of the tallest and the tallest of the shortest are in the same row. The shortest of the tallest people in each row is obviously the tallest person in his row, so he's taller than the tallest of the shortest, who is also in his row.

The third case is that the shortest of the tallest and the tallest of the shortest are in the same column. The tallest of the shortest people in each column is obviously the shortest person in his row, so he's shorter than the shortest of the tallest, who is also in his column.

The fourth case is that the shortest of the tallest is neither in the same column nor the same row as the tallest of the shortest. For this case, consider the person X who is standing in the intersection of the row containing the shortest of the tallest and the column containing the tallest of the shortest. X must be taller than the tallest of the shortest, since the tallest of the shortest is the shortest in his column, and X must also be shorter than the shortest of the tallest, since the shortest of the tallest is the tallest in his row. So TofS < X < SofT.

So the shortest of the tallest in each row is always taller than, or the same height as, the tallest of the shortest in each column.
 
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?

There's the same amount of lemonade in the orange juice as orange juice in the lemonade. Each cup ends with the same volume of liquid that it started with, and there's still an equal amount of each juice between the two cups.
 
All of my flowers except two are roses. All of my flowers except two are tulips. All of my flowers except two are daisies. How many flowers do I have?

Alternate Solution #1

Three: one rose, one tulip, and one daisy.

Alternate Solution #2

Two, neither of which are roses, tulips, or daisies.
 
Three humans and three monkeys (one big, two small) need to cross a river. But there is only one boat, and it can only hold two bodies (regardless of their size), and only the humans or the big monkey are strong enough to row the boat. Furthermore, the number of monkeys can never outnumber the number of humans on the same side of the river, or the monkeys will attack the humans. How can all six get across the river without anyone getting hurt?

The big monkey rows a small monkey over; the big monkey comes back. The big monkey rows the other small monkey over; the big monkey comes back. Two humans row over; a human and a small monkey come back. (Now two humans, the big monkey, and a small monkey are on the starting side of the river, and the third human and the second small monkey are on the destination side.) human and the big monkey row over; the human and a small monkey come back. Two humans row over; the big monkey rows back. (Now all the monkeys are on the starting side of the river, and all the humans are on the destination side.) The big monkey rows a small monkey over; the big monkey comes back. Then the big monkey rows the other small monkey over.
 
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