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

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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 basic grid of squares so universal to video games around the globe. And, extra importantly, the attention-grabbing arithmetic in the back of it. From the Knight's journey challenge and Queens Domination to their many diversifications, John Watkins surveys the entire recognized difficulties during this strangely fertile quarter of leisure arithmetic. Can a knight stick with a direction that covers each sq. as soon as, finishing at the beginning sq.? what number queens are wanted in order that each sq. is focused or occupied by means of one of many queens?

Each major subject is taken care of intensive from its old belief via to its prestige this day. Many appealing ideas have emerged for simple chessboard difficulties given that mathematicians first 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 third-dimensional chessboards or even chessboards on strange surfaces reminiscent of toruses (the an identical of enjoying chess on a doughnut) and cylinders. utilizing the hugely visible language of graph thought, Watkins lightly courses the reader to the vanguard of present study in arithmetic. via fixing the various many routines sprinkled all through, the reader can percentage totally within the pleasure of discovery.

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

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