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Mathematics in Chess - Combinatorics

#3

Nice job explaining the combinatorics behind chess960.

Just wanted to point out that whenever you ask "In how many ways... ?" combinatorics will offer methods and answer to this question. You can ask, for example, "In how many ways can I arrange my shoes?" or "In how many ways can I give gifts to a group of friends?". In the conclusion of the blog post it is said that maths and chess are "so interconnected" but I would argue that chess is not particularly special in that sense since combinatorics is there to offer an answer whenever you ask "In how many ways...?" in whatever field of interest.

Since it is an introductory article to combinatorics, I would suggest to furthermore clarify what "combinations" are and why binomial coefficients like 5C2 are the solution to the question at hand. And also what factorial "!" means.

Nice job explaining the combinatorics behind chess960. Just wanted to point out that whenever you ask "In how many ways... ?" combinatorics will offer methods and answer to this question. You can ask, for example, "In how many ways can I arrange my shoes?" or "In how many ways can I give gifts to a group of friends?". In the conclusion of the blog post it is said that maths and chess are "so interconnected" but I would argue that chess is not particularly special in that sense since combinatorics is there to offer an answer whenever you ask "In how many ways...?" in whatever field of interest. Since it is an introductory article to combinatorics, I would suggest to furthermore clarify what "combinations" are and why binomial coefficients like 5C2 are the solution to the question at hand. And also what factorial "!" means.
#4

Wobbly Demon,

My intention of this post was not to introduce combinatorics as a whole, but rather to put it into perspective with chess. When I say that maths and chess are so interconnected, I'm trying to portray a connection between the two when by perception there apparently is none or when a small relationship exists. I'm expecting that the basic knowledge of combinatorics and mathematics is there, such as the factorial operation and the differentiation between permutations and combinations.

Wobbly Demon, My intention of this post was not to introduce combinatorics as a whole, but rather to put it into perspective with chess. When I say that maths and chess are so interconnected, I'm trying to portray a connection between the two when by perception there apparently is none or when a small relationship exists. I'm expecting that the basic knowledge of combinatorics and mathematics is there, such as the factorial operation and the differentiation between permutations and combinations.
#5

Thanks for the explanation i think everyone needed this.

Thanks for the explanation i think everyone needed this.
#6

Could I ask? How can I calculate the number of the starting position, or on what it depends?

Could I ask? How can I calculate the number of the starting position, or on what it depends?
#7

@Leo-Skrypachov said in #6:

Could I ask? How can I calculate the number of the starting position, or on what it depends?

This is tricky --- there is a specific formula that is used to calculate the number. You can search the web or ask an AI for a good explanation and walkthrough of the specific algorithm used. I do not plan to cover this method, so please resort to the aforementioned ways of researching this question.

@Leo-Skrypachov said in #6: > Could I ask? How can I calculate the number of the starting position, or on what it depends? This is tricky --- there is a specific formula that is used to calculate the number. You can search the web or ask an AI for a good explanation and walkthrough of the specific algorithm used. I do not plan to cover this method, so please resort to the aforementioned ways of researching this question.