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Enjoy Puzzling with BiLLies

Paulus Gerdes
Publication Date: 
Number of Pages: 
[Reviewed by
Charles Ashbacher
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Paulus Gerdes has written three books about a new kind of puzzle. This is a joint review of

Puzzle Fun With biLLies
More Puzzle Fun With biLLies
Enjoy Puzzling with biLLies

The set of polynominoes known as biLLies are formed by combining two L trominoes L-tromino, bi-L, hence biLLies. The shapes are hexominoes and there are fourteen members in the set:


To paraphrase Andy Liu in the classic book by Golomb, “This number is large enough to be interesting yet small enough not to be overwhelming.”

All three of these books present a set of shapes that are to be constructed using the set of biLLies, there are 100 problems with six solutions in Puzzle Fun With biLLies, 100 problems with five solutions in More Puzzle Fun With biLLiesEnjoy Puzzling With biLLies has a different format, the shapes are presented followed by at least one solution. Interesting characteristics of the solution(s), such as an internal symmetry, are also mentioned.

If you are someone that enjoys doing puzzles with manipulatives, then these are books you will love. They present an entirely new category of such problems and unless you are really good at them or have a computer programmed to solve them, it could take a long time before you can solve them all.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.

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