Download Across the Board: The Mathematics of Chessboard Problems by John J. Watkins PDF

By John J. Watkins

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

Each major subject is taken care of extensive from its historic belief via to its prestige this present day. Many attractive options have emerged for easy chessboard difficulties on account that mathematicians first all started 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 equivalent to toruses (the an identical of enjoying chess on a doughnut) and cylinders. utilizing the hugely visible language of graph idea, Watkins lightly publications the reader to the leading edge of present learn in arithmetic. via fixing a number of the many routines sprinkled all through, the reader can percentage totally within the pleasure of discovery.

Showing that chess puzzles are the start line for very important mathematical principles that experience resonated for hundreds of years, Across the Board will captivate scholars and teachers, mathematicians, chess fans, and puzzle devotees.

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