Ponder This: November’s Challenge!

Are you a professional problem solver? If so, we invite you to submit your “Ponder This” solution for this month’s challenge.  Ponder This is IBM Research’s monthly brain-twister where you can match wits with some of the best minds at IBM.

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 than d1.
Bonus: Find more than three.

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IBM Research will post the names of those who submit a correct, original solution to their website! If you don’t want your name posted then please include such a statement in your submission. Send your submission to the webmaster.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: webmster@us.ibm.com

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