Can a King Outside a Square Stop a Pawn from Promotion on a Chessboard?

[ukamle]

There is a 64 square chessboard. A pawn is at some position on the checkboard. There are only two players on the checkboard: the pawn and king of opposing team. Imagine diagonals drawn from the pawn to the last rank on the chess board. Imagine a square formed by the ends of the diagonals. Prove that if King is outside the square, it can never stop the pawn from promotion (reaching the last rank).

 

[T.Rex]

N-queens contest next week.

Hi,
I think the proof has been provided since ages.
I have a book of Capablanca (first part of XX century) that explains that.

By the way, there is a contest next week for finding the solution to the "N queens" problem with N > 23 .
Look at:
http://www.etsi.org/plugtests/Upcoming/GRID/GRIDcontest.htm

" ...for the largest chessboard of dimension N, count the number of solutions for placing non-threatening N queens. The world record is for N=23, having 24,233,937,684,440 solutions. Winners are expected in the range of 24 to 27."

Pure Java. Grid over the world.

Tony

 

[tacman]

This is a classic chess problem that can be solved using mathematical principles. First, let's define the terms "pawn" and "king" in this context. In chess, a pawn is a piece that can only move forward one square at a time, except for its first move where it can move two squares. The king, on the other hand, can move in any direction but only one square at a time.

Now, let's look at the scenario described in the problem. We have a pawn on a 64 square chessboard, with a king of the opposing team. The pawn is trying to reach the last rank of the chessboard, which is the eighth rank. The diagonals drawn from the pawn to the last rank create a square, and the king is outside of this square.

To prove that the king can never stop the pawn from promotion, we must consider the movement capabilities of both pieces. As mentioned earlier, the pawn can only move forward, while the king can move in any direction. However, the king can only move one square at a time, and since it is outside of the square formed by the diagonals, it cannot reach the pawn in time to stop it from reaching the last rank.

To further understand this, let's consider the different scenarios that could occur. If the king moves closer to the pawn, the pawn can simply move forward and continue towards the last rank. If the king moves in a direction away from the pawn, the pawn can still move forward and reach the last rank. And if the king moves in a diagonal direction towards the pawn, the pawn can simply move forward along the other diagonal and still reach the last rank.

In all of these scenarios, the king is unable to reach the pawn in time to stop it from reaching the last rank. This is because the king can only move one square at a time and is outside of the square formed by the diagonals. Therefore, it is mathematically proven that if the king is outside of the square formed by the diagonals, it can never stop the pawn from promotion.

In conclusion, this chess problem illustrates the importance of understanding the movement capabilities of different chess pieces and how they can be used to solve mathematical problems. By analyzing the movement possibilities of the pawn and king in this scenario, we can prove that the king outside of the square formed by the diagonals can never stop the pawn from reaching the last rank.