New PDF release: Across the Board: The Mathematics of Chessboard Problems

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 uncomplicated grid of squares so universal to video games around the globe. And, extra importantly, the interesting arithmetic at the back of it. From the Knight's journey challenge and Queens Domination to their many diversifications, John Watkins surveys the entire famous difficulties during this unusually fertile zone of leisure arithmetic. Can a knight stick to 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 focused or occupied via one of many queens?

Each major subject is taken care of extensive from its historic belief via to its prestige this day. Many appealing recommendations have emerged for uncomplicated chessboard difficulties given that mathematicians first all started engaged on them in earnest over 3 centuries in the past, yet such difficulties, together with these regarding polyominoes, have now been prolonged to 3-dimensional chessboards or even chessboards on strange surfaces reminiscent of toruses (the similar of enjoying chess on a doughnut) and cylinders. utilizing the hugely visible language of graph concept, Watkins lightly courses the reader to the leading edge of present examine in arithmetic. via fixing a few of the many routines sprinkled all through, the reader can proportion totally within the pleasure of discovery.

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

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Across the Board: The Mathematics of Chessboard Problems (Princeton Puzzlers) by John J. Watkins

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