A facility is to be designed with 7 departments DlD7 such th

A facility is to be designed with 7 departments (Dl-D7) such that the following departments are adjacent (share a common wall): Dl is adjacent to D2, D3 and D4. D2 is adjacent to D5 and D6. D3 is adjacent to D4, D5 and D6. D4 is adjacent to every department. D5 is adjacent to D6 & D7. And D6 is adjacent to D7. Is it possible to design such a facility? Why or why not?

Solution

Given that D₄ is related to all the D_is.As adjacency is a symmetric relation,(for example) D₂ must also be adjacent to D₄ , which is not the case here. Hence the design is not possible.