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Neurobics: Cubical Condos

Kim, Scott Ph.D.

doi: 10.1097/01.NNN.0000392629.92680.8f
Departments: The Waiting Room

This puzzle exercises your ability to visualize three-dimensional shapes.

Walking down the street one day you pass by Cubical Condos, a condominium complex under construction in which every room is a perfect cube. Below is the unfinished frame of the building showing the outlines of the rooms. There are twenty-seven rooms in the building: nine rooms on each of the three floors. Customers can order a custom-configured condo containing two to eight rooms.

  1. The red girders outlines a luxury condo, which has eight rooms arranged in a two-story cube. How many different places could a luxury condo be configured within the twenty-seven room building?
  2. Figure

    Figure

  3. The blue girders outline two different mid-range condos, which each have four rooms arranged in a square. Notice that mid-range condos can be one or two stories tall. How many different places could a mid-range condo be configured within the building?
  4. Figure

    Figure

  5. The green girders outline two different economy condos, which each have two rooms arranged either side by side or one above the other. How many different places could an economy condo be configured within the building?
  6. Figure

    Figure

This puzzle was adapted from my 2011 Mind Benders and Brainteasers Page-a-Day calendar, published by Workman Publishing.

—Scott Kim

scott@scottkim.com

©2010 American Academy of Neurology