Find the Number of Cubes Removed

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A rectangular solid consists of small white cubes. A number of the cubes are removed by punching out all the cubes in the designated columns from front to back, top to bottom, and side to side. Find the number of removed cubes.
Contributed by: Izidor Hafner (January 2012)
Open content licensed under CC BY-NC-SA
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Reference
[1] Canadian Mathematics Competition: Problems, Vol. 4, Waterloo, Ontario, Canada: University of Waterloo, 1991 p. 59, problem 1990-G7-25.
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"Find the Number of Cubes Removed"
http://demonstrations.wolfram.com/FindTheNumberOfCubesRemoved/
Wolfram Demonstrations Project
Published: January 6 2012