Thread: nxn grid problem.
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Old October 30th, 2009, 10:42 AM
Soroban Soroban is offline
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Hello, theNoodler!

Quote:
Imagine you have a n\times n 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: \begin{array}{c}X \,=\, \text{black} \\ O \,=\,\text{white}\end{array}

. . \begin{array}{c}OOO\\OOO\\OOO\end{array} \qquad \begin{array}{c} XOO\\ OOO\\OOO \end{array} \qquad \begin{array}{c}XXO\\OXX \\ OXO \end{array}\qquad \hdots\text{ etc.}

I was told for this it would be 2^9 \,=\,512, 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: .2^9 \,=\,512 possible choices you can make.


Quote:
What if I had a 6x8 grid grid?

You have 48 cells to fill with 2 options each.

There will be: .2^{48} possible choices.
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