chess problem (mathematical)

[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]

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