Floor Plans

Geometry Level 2

Ahmed lives in a house built on a square-shaped land. As shown, it has 6 rooms which are all squares themselves! Charlie, who also has a square-shaped plot, likes Ahmed's idea and is trying to design a house where he wants exactly three rooms--a bedroom, a kitchen, and a drawing room.

Can Charlie make sure that all three of them are square rooms?

Ahmed's House Ahmed's House


Inspiration: Kitchen! by Micah Gadbois

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1 solution

Ojasvi Sharma
Sep 1, 2017

As the square land can be divided into 9 small squares, it would be impossible for Charlie to build 3 square rooms. Atleast one of them would be a rectangle.

But why must Charlie use this subgrid to construct his squares?

Agnishom Chattopadhyay - 3 years, 9 months ago

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Whatever may be the subgrid, Charlie will never be able to make his all three rooms of square shape which was asked in the question. Some space will always be left out.

Ojasvi Sharma - 3 years, 9 months ago

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