Three 3-digit non leading zero positive base N integers
P,
Q
and
R, with
P >
Q >
R, are such that:
- Q is the geometric mean of P and R, and:
- P, Q and R can be derived from one another by
cyclic permutation of digits.
Determine all possible positive integer values of N < 30 for which this is possible.
How many unique shapes can you get by unfolding a paper cube?
You can only cut along edges, and the shape must be in one piece and flat. By unique, I mean rotations and reflections don't count.
This problem can be analogized to four dimensions as well. How many unique 3-dimensional shapes can be made by "unfolding" a 4-dimensional hypercube into 8 cubes? This problem is significantly more difficult than the first.
Latest: 
Bonus: 
