I asked about this a while ago, but I'm still unsure. Imagine you have a nxn grid (3x3 for argument). I want to know how I can work out the total number of patterns I can make with 2 colours, say black and white. An example would be:
x = black o = white
ooo xoo xxo
ooo ooo oxx
ooo ooo oxo
So, pattern one is all white, patter two has one bit black etc. I was told for this it would be 2 to the 9th, giving me 512, which can't be correct! Is it 9 squared, giving me 81? What if I had a 6x8 grid, or 17x31 grid?
I did try to host a nicer picture than my x and o, but sadly I can't get imageshack to work.
Look at that attached graph. There are two grids.
Are they different colorings?
Maybe not. Rotate I counter-clockwise. We get II.
Now are they different?
If I & II are different then there are possible colorings.
If I & II are not different then you must tell us why?
Imagine you have a grid (3x3 for argument).
How can I work out the total number of patterns made with 2 colours, say black and white.
An example would be:
I was told for this it would be , which can't be correct!
. . Why not?
For each of the 9 cells, you have two choices: place a Black or place a White.
So you have 9 decisions with 2 options each.
. . There will be: . possible choices you can make.
What if I had a 6x8 grid grid?
You have 48 cells to fill with 2 options each.
There will be: . possible choices.