Counting
Algebra / Sequences and Series
Geometry
Logic
Miscellaneous
100
If you flip a fair coin 4 times, what is the probability that you will get exactly 2 tails?
4! / (2! 2!) = 6
24 = 16
6/16 = 3/8
100
Solve the system of equations:
3x + 2y = 12
6x - 4y = 18
x = 3.5, y = 0.75
100
What is the area of a triangle with vertices at (1, 2), (5, 2), and (5, 8)?
12
100
69
100
What is the name of the toy cowboy in Toy Story?
Woody
200
In a certain country telephone numbers have 9 digits. The first two digits are the area code (03) and are the same within a given area. The last 7 digits are the local number and cannot begin with 0. How many different telephone numbers are possible within a given area code in this country?
107 - 106 = 9,000,000
200
In an arithmetic series, a1 = 2 and a23 = 68. What is a16?
47
200
A 15 meter pole is held down from the top of a structure. At the end of the pole, another pole of length 18 meters is extended from that point until the bottom of the structure. The angle between the two poles is 34 degrees. How tall is the structure? (To the nearest meter)
10
200
Fill in the blank spots so that the sum of the numbers in each sector are equal. The sum of the 8 numbers in each circular rim must be the same as well.
200
If it were two hours later, it would be half as long until midnight as it would be if it were an hour later. What time is it now?
9 PM
300
How many different words can be created by rearranging the letters in SELFIESTICK?
11! / 23 = 4,949,600
300
What is the value of
11/7
300
Find the minimum distance from the point (−2, 5) to the circle (x − 10)2 + (y + 11)2 = 49
13
300
19! has how many zeroes at the end?
3
19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2, Find multiples of 10
300
“___” House on the Prairie
Little
400
How many words can be made by rearranging aabbccdd, such that no ’a’ appears somewhere to the right of some ’c’?
8! / (2! 2! 4!) = 420
400
A sequence of numbers starts with 1, 2, and 3. The fourth number of the sequence is the sum of the previous three numbers in the sequence: 1 + 2 + 3 = 6. In the same way, every number after the fourth is the sum of the previous three numbers. What is the eighth number in the sequence?
68
400
What is the sum of the angles in a icositetragon (24-sided)?
(24 - 2) * 180 = 3960
400
Isaac and Albert were excitedly describing the result of the Third Annual International Science Fair Extravaganza in Sweden. There were three contestants, Louis, Rene, and Johannes. Isaac reported that Louis won the fair, while Rene came in second. Albert, on the other hand, reported that Johannes won the fair, while Louis came in second.
In fact, neither Isaac nor Albert had given a correct report of the results of the science fair. Each of them had given one correct statement and one false statement. What was the actual placing of the three contestants?
Johannes won the fair, Rene came in second, and Louis came last.
If Louis won the fair, then Rene did not come in second. Also, Johannes would have won the fair since Louis cannot come in second. This is a contradiction.
If Rene came in second, then Louis did not win the fair. Johannes would have won the fair (since Louis cannot come in second if Rene is already in second). Therefore, Johannes won the fair, Rene came in second, and Louis came last.
400
Who discovered pi for the first time?
Archimedes
500
Is 22019 - 1 a prime number?
500
A unit of blood expires after 10! = 10 * 9 * 8 ... 1 seconds. Yasin donates a unit of blood at noon of January 1. On what day does his unit of blood expire?
Feb 12
500
A circle circumscribes a triangle with side lengths 28, 96, and 100. Determine the area of the circle.
2500 * pi
Note that this triangle is right (if you divide the sides by 4, you get 7-24-25, a well-known right triangle with integer side lengths). The right angle subtends an arc of 180 degrees, so the hypotenuse goes through the center of the circle. So the radius of the circle is 100/2 = 50, so the area of the circle is 2500 * pi
500
An Arab sheikh is old and must will his fortune to one of his two sons. He makes a proposition. His two sons will ride their camels in a race, and whichever camel crosses the finish line last will win the fortune for its owner. During the race, the two brothers wander aimlessly for days, neither willing to cross the finish line. In desperation, they ask a wise man for advice. He tells them something; then the brothers leap onto the camels and charge toward the finish line. What did the wise man say?
The man told the brothers to switch camels.
500
What’s the word with the most number of definitions?
run