Geometry
What is the name of this theorem: a2 + b2 = c2
Pythagorean Theorem
As of 2023, how many McDonalds' are there in the world?
41,822
What is the 13th prime number?
41
A must ferry a wolf, a goat, and a cabbage across a river. His boat can only carry one item at a time besides himself. If left alone, the wolf eats the goat or the goat eats the cabbage. How does he get all three across safely?
1. Take the goat across.
2. Return, take the wolf across, and bring the goat back.
3. Take the cabbage across, return, and bring the goat across.
How many sides does a dodecagon have?
How tall is the Empire State building (in feet, including spire + antenna)?
Who is considered the first female mathematician?
Hypatia of Alexandria
You are outside a room with three light switches. Inside the room are three light bulbs, each controlled by one switch. All of the light bulbs are turned off before you begin. You may only enter the room once. How can you determine which switch controls which bulb?
Turn on two bulbs (A, B) for a long time, then shut one of them off (A). The lit bulb is the one that was on the whole time (B). Out of the two unlit bulbs, one (A) will be warm and the other (C) will be cool.
(4/3)πr2
How many babies are born each hour?
15,000
Fill in the blank: ____ Elements (famous math book)
Euclid's
You have three bowls: 7L, 4L, and 3L. If you start with 7L in the 7L bowl, what is the quickest way you can obtain 2L, 2L, and 3L?
Fill the 4L using the 7L bowl. Leaves 3L in the 7L bowl.
Fill the 3L using the 4L bowl. Leaves 1L in the 4L bowl.
Pour the 3L in the 3L bowl into the 7L bowl. Now there are 6L in the 7L bowl.
Pour the 1L in the 4L bowl into the 3L bowl. Now there is 1L in the 3L bowl and the 4L is empty.
Fill the 4L using the 7L bowl. Leaves 2L in the 7L bowl.
Fill the 3L using the 4L bowl. Now there are 2L in the 7L bowl, 2L in the 4L bowl, and 3L in the 3L bowl.
What is the sum of the interior angles of a hexagon?
720 degrees
How many benches are in Central Park?
10,000
How many zeroes does googolplex have?
Four people must cross a bridge at night in 1, 2, 7, and 10 minutes. Only two can cross at a time, and they must use a single torch. Thus, each pair travels at the slower person’s speed. What’s the fastest total time and how?
17 minutes. 1 and 2 cross, 1 returns, 7 and 10 cross, 2 returns, and 1 and 2 cross.
What shape has 30 rectangular faces, 20 triangular faces, and 12 pentagonal faces?
What is the rhombicosidodecahedron?
How many tigers remain in the wild?
5,574
According to the film The Hitchhiker’s Guide to the Galaxy, this number is associated with life, the universe, and everything.
42
You have a balance scale and 12 coins, 11 of which are genuine and identical in weight; but one is counterfeit, and is either lighter or heavier than the others. How can you determine the counterfeit coin and whether it is lighter or heavier in the least amount of weighings? (you'll need an explanation!)
It will take three weighings.
First, group the coins in three groups of 4 (1-4, 5-8, 9-12). Weigh groups 1-4 and 5-8 against each other. Case 1: If the scale is balanced, those eight coins are all genuine. Proceed by weighing any two genuine coins against coins 9 and 10; if they balance, one of coins 11 and 12 is the counterfeit. Otherwise, one of coins 9 and 10 is counterfeit. Out of the two possible fakes, simply weigh one of them against a genuine coin and you'll know which is the counterfeit and whether it is light or heavy. (another option is to weigh three genuine against three unknown and go from there)
Case 2: If the scale is not balanced after the first weighing, we know that coins 9-12 are all genuine. WLOG, say that coins 1-4 are lighter than coins 5-8. The counterfeit is either one of 1-4 and light, or one of 5-8 and heavy. Weigh coins 1, 2, 5 against 3, 6, 9 (or any other genuine coin) for the second weighing. If balanced, then the counterfeit is either 4 (heavy), 7 (light), 8 (light). Weigh 7 against 8; if balanced, 4 is the counterfeit, otherwise, the lighter coin is the counterfeit. If the second weighing was not balanced and the 1, 2, 5 group was heavier, then the counterfeit is 1 (heavy), 2 (heavy), or 6 (light). Weigh 1 against 2; if balanced, 6 is the counterfeit, otherwise, the heavier coin is the counterfeit. If the second weighing was not balanced and the 3, 6, 9 group was heavier, either 3 (heavy) or 5 (light) is the counterfeit. Weigh either one against a genuine coin to find the counterfeit.