Long Riddles

Long riddles with answers test your problem solving skills. These lengthy puzzles test your ability to piece together information and find the answer.

4 Days for School

A student has missed an excessive number of days at school and thus the principal called him to his office and requested for an explanation.

The student said, “There just isn’t enough time for school. I need 8 hours of sleep a day, which adds up to about 122 days a year. Weekends off is 104 days a year. Summer vacation is about 60 days. If I spend about an hour on each meal, that’s 3 hours a day or 45 days a year. I need at least 2 hours of exercise and relaxation time each day to stay physically and mentally fit, adding another 30 days. Add all of that up and you get about 361 days. That only leaves 4 days for school.”

The principal is confused, but can’t figure out why. What is wrong with the student’s argument?

Riddle Answer

The Three Gods

Three Gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter.

Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one God. The Gods understand English, but will answer all questions in their own language, in which the words for yes and no are “da” and “ja”, in some order. You do not know which word means which.

It could be that some God gets asked more than one question (and hence that some God is not asked any question at all).
What the second question is, and to which God it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
Random will answer “da” or “ja” when asked any yes-no question.

What would your three questions be?

Riddle Answer

King and 3 Hats

The King calls in three wise men and tells them to all close their eyes. While their eyes are closed, he goes around and puts a hat on each of them.

“I put a blue or white hat on each of you,” the King says. “I won’t tell you what color each hat is, but I promise you that at least one of you has a blue hat.”

“Now open your eyes,” he continues. “You may not communicate with each other at all. Within one hour, one of you must call out the color of your own hat. If you aren’t able to do this, or if anyone calls out the wrong color, I will have you all exiled from the kingdom.”

The wise men open their eyes and look at the other mens’ hats. They stand there for almost the whole hour in silence, thinking. Just as time is about to run out, all three men figure out the color of their own hats and yell the colors out at the same time.

You can assume that all three men are perfect logicians, that they know that the others are perfect logicians, and that they all think at the same speed.

What colors are the three men’s hats?

Riddle Answer

Two Mathematicians Puzzle

Two mathematicians, Tom and Smith are walking down the street.

Tom: I know you have three sons. What are their ages?
Smith: The product of their ages is 36.
Tom: I can’t tell their ages from that.
Smith: Well, the sum of their ages is the same as that address across the street.
Tom: I still can’t tell.
Smith: The eldest is visiting his grandfather today.
Tom: Now I know their ages.

Do you know the age of the kids?

Riddle Answer

Peas and Lentils

A poor farmer went to the market to sell some peas and lentils. However, as he had only one sack and didn’t want to mix peas and lentils, he poured in the peas first, tied the sack in the middle, and then filled the top portion of the sack with the lentils.

At the market a rich innkeeper happened by with his own sack. He wanted to buy the peas, but he did not want the lentils.

Pouring the seed anywhere else but the sacks is considered soiling. Trading sacks is not allowed. The farmer can’t cut a hole in his sack.

How would you transfer the peas to the innkeeper’s sack, which he wants to keep, without soiling the produce?

Riddle Answer

Long Riddles

4 Days for School

The Three Gods

King and 3 Hats

Two Mathematicians Puzzle

Peas and Lentils

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