Math problems applied in chess.

Hello! When it comes to Mathematics and Chess, surely all or many people will be familiar with two famous problems: ''Knight's Tour Problem'' and ''Rice and Chessboard''. But few people know that Chess has many tricky problems, just like the plot of Sherlock Holmes movies, full of puzzles and thinking.

And two of the many chess problems I'm going to tell you about today were in my curriculum when I was in grade 12 and preparing for college. These accidental discoveries were made when I accidentally found some documents of famous Math teachers in the country where I live.

And one of these two Math problems actually appeared in one of our exams, which was given by the City where I live. In the competition cluster exam of high schools.

The math problems that I am about to give are all in Vietnam where I am living and studying. So all the pictures of the problems are written in Vietnamese.

Problem 1: Probability and statistics. Practical application through a chess match between two players Le Quang Liem and Magnus Carlsen.

The question is translated into English as follows: ''In a chess match between two players Le Quang Liem and Magnus Carlsen, each game will have only one winner and one loser, no draw (if there is a draw, lots will be drawn to find out who is the winner of that game). Knowing that in each game, the probability that Le Quang Liem wins is 0.4; the probability that Magnus Carlsen wins is 0.6. Each win is counted as 1 point for the player, the loser will not get any points. If anyone creates a difference of 2 points, they will win the final victory, calculate the probability that Le Quang Liem is the final winner.''

Problem 2: Apply integration to calculate the volume of a Pawn.

The question is as follows: ''A model of a pawn on a chess board is a rotating circular block with a cross-section through the axis as follows: the head of the chess piece is a part of a sphere with radius (√2) (cm); curves AB and EF are part of a parabola with vertices B and E; DE and BC are a quadrant of a circle with radius 1cm. Calculate the volume of the pawn model (unit cm³ and the result is rounded to the nearest unit.)'' 

Solution to this problem:

Problem 3: Statistical probability, applied in the problem of the king returning to the starting square.

The problem is as follows: ''A king is placed on a square in the middle of the chessboard. Each move, the king is moved to another square that is adjacent to or on top of the square it is on (see illustration). An randomly moves the king 3 steps, calculate the probability that after 3 steps the king returns to the starting square.''

Solution to this problem:

Problem 4: Geometric progression, application of geometric progression in chess.

The problem is as follows: On a chess board as shown, Pawn, Knight, Bishop, Rook, Queen are counted as 1, 3, 3, 5, 9 respectively. Suppose the Pawn is in position e5 and will be promoted to Queen at position h8, then the Pawn (moving in a straight line and capturing diagonally) will capture the chess pieces in order with the number of points forming a geometric progression. What is the total number of points captured by the Pawn?

That's it, if you find these problems appealing to you, then take out a pen and paper and think about how to solve them! Thanks.