## Review: Train Your Brain: A Year’s Worth of Puzzles

Some books are hard to review. This one isn't. Train Your Brain: A Year's Worth of Puzzles is the kind of book where you look at a few of its puzzles. If they intrigue you, you'll like the book. Simple enough.

Here's one puzzle.

Knight on the Chess Board. We would like to move a knight across the chess board so that we go from the lower-left corner to the upper right corner, landing in the process on each square exactly once. Is this problem solvable?

This is a great puzzle that I'll use in my Math circles. It's a nice little exploration and it generalizes well to make it harder for folks who solve it very quickly. For those who get stuck there is a hint on a different page so that the hint is not right in front of you.

Author George Gratzer has a nice compilation of varied Math and logic puzzles. The book is divided into 52 chapters, one for every week of the year. The first 36 chapters each have three puzzles. The remaining 16 are "Black Belt" chapters, with two puzzles in each of those.

Here's a black belt problem.

An interesting game. This is a game for two people. Players take turns laying down quarters on a rectangular table until no more coins fit on the table top. coins may touch but may not overlap each other. The winner is the player who places the last coin on the table. Is there a winning strategy for the player who goes first?

I like the book. The puzzles are very clever. Many are elegant in that the problem is easy to state and the right insight will help to solve it easily. The author has written a number of books. The publisher's web-site tells about the author:

George Grätzer is a distinguished professor in the Department of Mathematics at the University of Manitoba. He has published over 200 research publications and 25 books, including General Lattice Theory and Math into LaTex. He is a member of the Canadian Academy of Sciences and an external member of the Hungarian Academy of Sciences.

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