1. ## How many patterns?

Hello.

Let's say you have a 4x4 grid, you can make patterns by using any number of squares, connected or not. So, one pattern may use just one square, top left, another may use one top right, another may use the entire top row etc. How many patterns can you make from that 4x4 grid?

Cheers.

N.

2. Originally Posted by theNoodler
Let's say you have a 4x4 grid, you can make patterns by using any number of squares, connected or not. So, one pattern may use just one square, top left, another may use one top right, another may use the entire top row etc. How many patterns can you make from that 4x4 grid?
There are a great many ways that one could read this question.
Let's say that we will use only one color, red, and the grid has a fixed orientation.
There are $\displaystyle 16$ sub-squares in a $\displaystyle 4\times 4$ grid.
So there are $\displaystyle 2^{16}$ subsets of those squares.

Is that what you are asking?

3. Hello.

OK, sorry, I'll try oto be more specific. We are using one colour.

One pattern could be:

XOOO
OOOO
OOOO
OOOO

another could be:

XXOO
OOOO
OOOO
OOOO

and yet another could be:

XOOO
XOOO
XOOO
XOOO

it's simply that a pattern could use one or all the squares, or any number in between, any orientation. Does that help?

Thanks.

4. Look at the graphic.
If that could one of the patterns, then the answer is still $\displaystyle 2^{16}$.

If not, you need to set out the rules.

5. Hello.

That is perfect, thank you.