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I have a $16\times16$ grid. $256$ squares.

In each square there can be a value from $1$-$256$.

How do I work out how many total combinations the complete grid could have?

I would like the know the formula so I can work it out for different grid sizes.

Teddy38
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Newbie Noob
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  • @KajHansen He says "combinations", so he may mean order doesn't matter, or might just not know the correct terminology. – Mark Schultz-Wu Nov 17 '16 at 08:44
  • Do you want to know how many different configurations there are for the grid? Also, can different cells have the same value? – RGS Nov 17 '16 at 10:08

4 Answers4

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EDIT (thanks for @RSerrao's comment): If, the values are distinc, you can think like this: the first cell can have 256 posibilities, the second cell can have 255 posibilities and so on. Then, you can get the formula.

If not, i.e. the values can be repeated, so each cell has 256 posibilities.

GAVD
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  • I think that by "combinations" he means configurations and it also looks like the values can be repeated. – RGS Nov 17 '16 at 10:06
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In my answer I assume that you want to know the total number of different configurations for the grid. Thus I assume that a grid that starts with $1, 2$ is different from one that starts with $2, 1$. I also assume that different cells can have the same value.

For each single space you have 256 options. Thus, if you have 16 rows and 16 columns, yielding 256 cells, you have $256^{16\cdot16} = 256^{256}$ total possible combinations.

RGS
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each square has 256 options you have 256 squares (Number_Of_Options_for_1_Instance)^(Number_Of_repetitions(Instances))
number of combinations = 256^256

Itay.V
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if you have a n*n grid then the total numbers you can use is n^2 , now at a first square u have chances (n^2)chances ,in the next you have (n^2-1) chances , in such a process the total set of combination you have (n^2)!.

soumya banerjee
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