Leonardo's Mirror & Other Puzzles The Monty Hall Problem & Other Puzzles I. Moscovich

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Ivan Moscovich, the author of the two books under review is a well known and much respected puzzlist and toy creator. The books - one of which first appeared in 1994, the other in 2004 - have been recently republished by Dover. Both books are lavishly and beautifully illustrated in full color and would make a memorable present.

Both books are more than mere collections of puzzles. Most of the puzzles are preceded with background information that sometimes is sufficiently comprehensive to occupy a whole page or two. The reader is treated to the shapes of planetary trajectories, a short biography of Leonardo da Vinci, and that of Leonardo of Pisa; quadrature of lunes and geometric dissections; the ideas of mechanical linkages and sphere packing; the Golomb rulers; paper-and-pencil games; and the Ramsey theory. The breadth of the collections and occasional depth are quite staggering.

What about the "puzzles" themselves? Say, in what sense Monge's theorem of three circles or visual illusions are puzzles? So, some "puzzles" are engaging math problems, others are thought provoking or plain, entertaining activities - these are combined into groups of 2-5. What makes them "puzzles" is their great diversity which keeps the reader continuously involved, puzzled and puzzling.

Some of the puzzles are well known, but many appear to be original. E.g., I do not remember seeing a Hex-like game played on a square grid in which the moves are those of the chess knight.

Solutions at the end of the books are similarly well illustrated and provide visual clues accompanied by textual explanations.

The level of the puzzles varies but - on the whole - the books will be appreciated by a broad readership of puzzle lovers as well as by the parents who would like to sprinkle the interaction with their kids with engaging (mostly) math activities. The books are so attractively made they could not fail but engross even young children's minds.

1. I. Moscovich, Leonardo's Mirror & Other Puzzles, Dover, 2011
2. I. Moscovich, The Monty Hall Problem & Other Puzzles , Dover, 2011

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