The Mathematics of Shuffled Cards

It is said that each time you shuffle a 52-card deck,  each arrangement you make may have never existed in all history, or may never exist again. Why? Because of the enormous number of arrangements that can be made using 52 distinct objects (in this case, cards).

To understand this, we can look at the number of arrangements that can be made with smaller number of objects. Lets start with 3 objects A, B, and C. The possible arrangements are ABC, ACB, BAC, BCA, CAB and CBA. Notice that for the first position, there are 3 possible choices (see figure below). Then, after you made the first choice, there are only 2 possible choices left. And after the second choice, you only have 1 possible choice. This means that the number of arrangements of 3 objects is 3 \times 2 \times 1 = 6Continue reading

How to Scientifically Cut a Cake

If you are a sugar-conscious family, then you would probably need to learn Sir Francis Galton’s way to cut a cake. According to Sir Galton’s letter to the editor to the 1906 journal Nature, the ordinary method of cutting out a wedge is faulty because it does not minimize the  exposure of the cake’s surface. Exposure of the interior of the cake for a period of time can make it dry.

Watch the video below and learn how to scientifically cut a cake so you can preserve its taste even if you eat it after a day.

Sir Francis Galton was an English polymath, psychologist,anthropologist, eugenicist, tropical explorer, geographer, inventor, meteorologist, proto-geneticist, psychometrician, and statistician. He was knighted in 1909.

The Honeybee and the Hexagon

Zack Patterson and Andy Peterson showcase a 3-minute video to introduce one of the smartest animals on the planet: bees. According to the video, scientists believe that bees comprehend the roundness of the earth, can calculate angles, and as we all know, build efficient honey storage space in hives which are in hexagonal in shape.

Watch the video below and see why bees are good geometers.

Finally, I want to leave you with this quote from The Bee Movie.

According to all known laws of aviation, there is no way that a bee should be able to fly. Its wings are too small to get its fat little body off the ground. The bee, of course, flies anyways. Because bees don’t care what humans think is impossible.

How Probability Can Be Used to Design Games of Chance

One of the origins of of probability as a field in mathematics was solving games of chance. The famous correspondence between Fermat and Pascal in 1654 was one of the earliest accounts on how to use mathematics formally in order to solve a fair game of chance.

In this post, we are going to design a game that will demonstrate the power of probability. We will use probability to create a game that looks like as if it favors the player, while in reality, it favors the casino. Although most casino games actually obviously favor the casino, the game below is a bit more conservative (or should I say ‘deceptive.’)

The dice to be used in the game below is the standard 6-sided die whose number of dots are from 1 to 6. This means that the smallest possible sum is 1 + 1 = 2 and the largest possible sum is 6 + 6 = 12. Below are the instructions on how to play the game.  Continue reading