math puzzles
logic puzzles
cs trivia
trick questions
100
Six farmers catch six lambs in six minutes.
How many farmers will be needed to catch sixty lambs in sixty minutes?
6
100
A boy and a girl are talking.
• "I am a boy" said the child with black hair.
• "I am a girl" said the child with white hair.
At least one of them lied. Who is the boy and who is the girl?
The child with the black hair is the girl, and the child with the white hair is the boy.
100
In most programming languages, which data type is best suited to store a value representing a simple true/false condition?
Boolean
100
Find a number with its letters in alphabetical order.
Example: "five" has "fiv" in alphabetical order, but not "e".
Forty
200
A solid, four-inch cube of wood is coated with blue paint on all six sides.
Then the cube is cut into smaller one-inch cubes.
These new one-inch cubes will have either three blue sides, two blue sides, one blue side, or no blue sides. How many of each will there be?
There are 8 with three sides colored, 24 with two sides colored, 24 with one side colored, and 8 with no sides colored.
200
A scientist gathered four math students. They were then lined up so that each one could see the one in front of them but not behind them. Each had a hat placed on their head.
So the student in the back could see the hats of the three students in front, but the student in front could not see any hats.
"There is a red hat, a white hat, a blue hat, and a hat that is a duplicate of one of those colors," the scientist said.
Starting with the one in the back, each student was asked what color hat they were wearing. They all gave the correct answer!
What was the arrangement of the hats that made this possible?
The two front students are wearing the same color hats, this is the only way all of the students could know what color hat they were wearing.
200
What is the decimal (base-10) equivalent of the 8-bit binary number 00001010?
10
200
An electric train is going 60 km/h north, the wind is blowing 40 km/h from the south. Which way is the train's smoke blowing?
What smoke?
It is an electric train.
300
You have three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble.
You pick a random bag and take out one marble.
It is a white marble.
What is the probability that the remaining marble from the same bag is also white
2/3 (not 1/2)
You know that you do not have Bag B (two black marbles) so there are three possibilities
You chose Bag A, first white marble. The other marble will be white
You chose Bag A, second white marble. The other marble will be white
You chose Bag C, the white marble. The other marble will be black
So 2 out of 3 possibilities are white.
Why not 1/2? You are selecting marbles, not bags.
300
There are three people (Alex, Brook and Cody), one of whom is a knight, one a knave, and one a spy.
The knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth.
Alex says: "Cody is a knave."
Brook says: "Alex is a knight."
Cody says: "I am the spy."
Who is the knight, who the knave, and who the spy?
Alex is a Knight
Brook is a Spy
Cody is a Knave
300
What are the four official competitive divisions in USACO, ordered from lowest to highest?
Bronze, Silver, Gold, and Platinum
300
The following equation is wrong: 101 − 102 = 1
Move one numeral to make it correct.
Move the numeral 2 half a line up to make 101 − 10² = 1
400
Sam saw that the oven digital clock was showing 1:23, and noticed that each number was one higher than the number to its left.
Sam wondered: of all the different clock times from 0:00 to 12:59, how many are like that?
0:12
1:23
2:34
3:45
4:56
12:34
400
You are at an unmarked intersection ... one way is the City of Lies and another way is the City of Truth.
Citizens of the City of Lies always lie.
Citizens of the City of Truth always tell the truth.
A citizen of one of those cities (you don't know which) is at the intersection. What question could you ask to them to find the way to the City of Truth?
You ask "In which of those two directions do you live?"
400
What animal famously stars in almost every word problem in USACO?
Bessie the Cow
400
What is unique about 8549176320 ?
It is the digits 0 to 9 in alphabetical order.
500
In Girlia a family is not considered complete until a girl is born.
So every family continues to have children until they have a girl.
What would the ratio of boys to girls be there?
(Assume that having a girl or boy is equally likely.)
1/2
500
The host, Monty Hall, offers you a choice of three doors. Behind one is a sports car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).
Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.
You cannot hear the goats from behind the doors, or in any way know which door has the prize.
Should you stay, or switch, or doesn't it matter?
Switch!
Your first choice has a 1/3 chance of having the car, and that does not change.
The other two doors HAD a combined chance of 2/3, but now a Goat has been revealed behind one, all the 2/3 chance is with the other door.
500
Which graph traversal algorithm typically uses a Queue data structure to explore neighbor nodes level by level?
Breadth First Search (BFS)
500
A criminal gets to pick his punishment by choosing among three rooms.
the first is full of burning fires,
the second is full of assassins with loaded guns,
the third is full of lions that haven't eaten in a year.
Which room is the safest choice?
The Third Room.
The Lions will be dead by now