Does the field of vision from 0,0 assume that it viewer is fixed at the exact center and only able to rotate? No accomodation for binocular vision like humans have with eyes slightly off the center on both sides? I think this is relevant in how many trees one can see past the blocking trees.
That interpretation would require additional parameters, like how far apart the two eyes are. The simplest interpretation of the puzzle is monocular vision, fixed at (0, 0), and free to rotate 360 degrees.
Your description of the braille solution is missing the long diagonals, i.e. two spots raised at opposite corners. Your description only includes small diagonals. The illustration you included is correct and includes every case.
The cases that were enumerated in detail were the translatable cases (so you could figure out how many of those to discard), and the long diagonals don't translate.
For the generic braille case, I found it easier to reason about the formula as:
Total number of patterns
- Patterns that could be translated up
- Patterns that could be translated left
+ Patterns that could be translated both left and up (that got subtracted twice so far)
= ((2^mn) - 1)
- ((2^(m-1)n) - 1)
- ((2^m(n-1)) - 1)
+ ((2^(m-1)(n-1)) - 1)
= 2^mn - 2^(m-1)n - 2^m(n-1) + 2^(m-1)(n-1)
Does the field of vision from 0,0 assume that it viewer is fixed at the exact center and only able to rotate? No accomodation for binocular vision like humans have with eyes slightly off the center on both sides? I think this is relevant in how many trees one can see past the blocking trees.
That interpretation would require additional parameters, like how far apart the two eyes are. The simplest interpretation of the puzzle is monocular vision, fixed at (0, 0), and free to rotate 360 degrees.
Your description of the braille solution is missing the long diagonals, i.e. two spots raised at opposite corners. Your description only includes small diagonals. The illustration you included is correct and includes every case.
The cases that were enumerated in detail were the translatable cases (so you could figure out how many of those to discard), and the long diagonals don't translate.
Good point, including those would just mean subtracting 0.
Do I have to be able to see the whole diameter of the tree, or just a part of it?
Pretty sure it's just a part.