– Solving a problem like the Tower of Hanoi requires a specific system of sequential moves. Such a series of instructions is called an algorithm and we learn in school algorithms for addition and multiplication. And a cookbook recipe for a chocolate cake is another example of an algorithm.

– Algorithms can be applied by machines. Even computer science is based on the study of algorithms.

– Algorithms must not only be correct, but also highly efficient. Their efficiency is measured by their length or number of steps.

The science of encryption and decryption is called cryptography. Throughout the ages, great efforts have been made to prevent enemies, competitors, or cyber thieves from eavesdropping on secrets where cryptography was used.

There is a discourse of unbreakable “quantum cryptography”, but it has not become a reality.

Harmonics is the branch of math that deals with “counting all sets”. Its problems are usually quite easy, but in our model, they are easy to solve. For each of the 3 leg images, there are 4 possible body images, so there are 3×4 = 12 combinations of legs and body. For each of them, there are 5 possible faces, so there are a total of 12×5 = 60 combinations.

In the 18th century, the great mathematician Euler had posed this problem to himself, referring to real bridges in the city of Queensburg. Exhausted from walking, Euler decided to analyze the problem mathematically. He proved that the problem was unsolvable and established an important branch called graph theory. Modern graph theory is a powerful tool for deriving common features of many seemingly unrelated problems, from the design of water networks to computer networks.

Map coloring is one of the most famous and researched issues in graph theory, it has many practical applications and many intuitions related to this issue and many computer scientists and mathematicians are still trying to decipher these intuitions.

This issue is the assignment of a “color” to one of the elements of the chart so that a set of specific conditions are met, perhaps the simplest formulation of this issue is to color the vertices of the chart so that no two adjacent vertices have the same color. This type of coloring is called “vertex coloring”, and similarly we know “side coloring” which is the coloring of sides so that no two sides that share a vertex have the same color, and “face coloring” in a planar diagram is assigning a color to each face or region so that no two regions that share the same boundary have the same color.

Harmonics and permutations are names by which mathematicians express certain combinations of objects or symbols. Permutations are organized arrangements of a set of objects, for example, (X.Y.Z), (X.Z.Y), and (Y.Z.X) are three permutations of the set of symbols X.Y.Z.

Combinations are those sets that contain the same objects regardless of order, so the sets (X.Y.Z), (X.Z.Y), and (Y.Z.X) are all the same combination, while the sets A.B.C., A.B.D., and A.C.D. are different combinations.