Across the Board: The Mathematics of Chessboard Problems - download pdf or read online

Across the Board is the definitive paintings on chessboard difficulties. it isn't easily approximately chess however the chessboard itself--that uncomplicated grid of squares so universal to video games all over the world. And, extra importantly, the interesting arithmetic in the back of it. From the Knight's journey challenge and Queens Domination to their many adaptations, John Watkins surveys all of the recognized difficulties during this unusually fertile zone of leisure arithmetic. Can a knight keep on with a course that covers each sq. as soon as, finishing at the beginning sq.? what number queens are wanted in order that each sq. is concentrated or occupied via one of many queens?

Each major subject is handled extensive from its historic perception via to its prestige this present day. Many attractive ideas have emerged for easy chessboard difficulties because mathematicians first begun engaged on them in earnest over 3 centuries in the past, yet such difficulties, together with these related to polyominoes, have now been prolonged to 3-dimensional chessboards or even chessboards on strange surfaces comparable to toruses (the an identical of taking part in chess on a doughnut) and cylinders. utilizing the hugely visible language of graph idea, Watkins lightly publications the reader to the vanguard of present learn in arithmetic. via fixing a few of the many routines sprinkled all through, the reader can percentage totally within the pleasure of discovery.

Showing that chess puzzles are the place to begin for vital mathematical rules that experience resonated for hundreds of years, Across the Board will captivate scholars and teachers, mathematicians, chess fans, and puzzle devotees.