The article explores the application of binary and ternarynumber systems to three classical mathematical puzzles –weight problem of Bachet deMeziriac, binary numbers magictrick, and the detection of a counterfeit coin. The article furtherelucidates the generalization of these puzzles using thebalanced number system.

The article delves into the realm of application of complex numbers and matrix transformations in pentagonal tiling. A basic understanding of the concepts in these two branches helps to plot the tiles in any computer algebra system (CAS). The application of the concepts has been demonstrated for the special case of Type 13 pentagonal tiling.