IBM Research | Ponder This | November 2013 challenges

# Ponder This

## November 2013

<<October November December>>

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)
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Archer (11/01/2013 09:40 PM EDT)
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