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During the 125th European Study Group with Industry held in Limassol, Cyprus,5-9 December 2016, one of the participating companies, Engino.net Ltd, posed avery interesting challenge to the members of the study group. Engino.net Ltd isa Cypriot company, founded in 2004, that produces a series of toy sets -- theEngino$^{\circledR}$ toy sets -- consisting of a number of building blockswhich can be assembled by pupils to compose toy models. Depending on thecontents of a particular toy set, the company has developed a number of modelsthat can be built utilizing the blocks present in the set, however theproduction of a step-by-step assembly manual for each model could only be donemanually. The goal of the challenge posed by the company was to implement aprocedure to automatically generate the assembly instructions for a given toy.In the present paper we propose a graph-theoretic approach to model the problemand provide a series of results to solve it by employing modified versions ofwell established algorithms in graph theory. An algorithmic procedure to obtaina hierarchical, physically feasible decomposition of a given toy model, fromwhich the assembly instructions can be recovered, is proposed.

Physically Feasible Decomposition of Engino$^{\circledR}$ Toy Models: A Graph Theoretic Approach