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Ponder This

November 2013

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Ponder This Challenge:

A three-dimensional cube has eight vertices, twelve edges, and six faces. Let's call them 0-D, 1-D, and 2-D faces, respectively.
Denote f(d,k) as the number of k-dimensional faces of an d-dimensional hyper cube, so f(3,1)=12.
Find three cubes (with different dimensions d1, d2, and d3) such that the number of k1, k2, and k3 dimension faces are the same, i.e. f(d1,k1) = f(d2,k2) = f(d3,k3).
We are looking for nontrivial solutions, so k1 should be less then d1.
Bonus: Find more than three.


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Challenge: 11/01/2013 @ 01:00 PM EST
Solution: 12/01/2013 @ 01:00 PM EST
List Updated: 11/26/2013 @ 01:00 PM EST

People who answered correctly:

Reiner Martin (11/01/2013 04:59 PM EDT)
Philipp Seemann (11/01/2013 05:04 PM EDT)
Antoine Comeau (11/01/2013 05:29 PM EDT)
Gilad Weiss (11/01/2013 05:31 PM EDT)
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Vladimir Sedach (11/01/2013 05:39 PM EDT)
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Lorenz Reichel (11/01/2013 06:28 PM EDT)
William Heller (11/01/2013 07:03 PM EDT)
Rick Kaye (11/01/2013 07:46 PM EDT)
Kan Shen (11/01/2013 08:30 PM EDT)
Don Dodson (11/01/2013 08:55 PM EDT)
Antonio García Astudillo (11/01/2013 09:28 PM EDT)
Archer (11/01/2013 09:40 PM EDT)
Cynthia Beauchemin (11/01/2013 10:01 PM EDT)
Seth Cohen (11/01/2013 10:54 PM EDT)
Dan Dima (11/01/2013 11:06 PM EDT)
Dheeraj Reddy (11/01/2013 11:23 PM EDT)
Nicholas Ngiam & Liu Ren Wei (11/01/2013 11:30 PM EDT)
Minxi Jiang (11/02/2013 12:52 AM EDT)
Manoj vedvistara (11/02/2013 01:08 AM EDT)
Sameer Mehta (11/02/2013 01:42 AM EDT)
Adam Kozdron (11/02/2013 01:53 AM EDT)
Robin Ryder (11/02/2013 01:57 AM EDT)
Michael Wilms (11/02/2013 02:08 AM EDT)
Stéphane Higueret (11/02/2013 03:00 AM EDT)
Michael Liepelt (11/02/2013 03:39 AM EDT)
Dezhi Zhao (11/02/2013 04:27 AM EDT)
Pawel Milewski (11/02/2013 04:38 AM EDT)
Adrian Orzepowski (11/02/2013 05:38 AM EDT)
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Anatoli Plotnikov (11/02/2013 06:56 AM EDT)
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Florian Fischer (11/02/2013 06:53 PM EDT)
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