'Formula for the number of possible image variations given the number of pixels?
It's probably been asked before but I can't find it. Assume you can only use two colors and are given a number of pixels. How many possible image variations are possible? For 1 pixel, it's 2. For 2 pixels, it's 4. For 3 pixels, it's 8. It looks like it's a 2 to the power of however many pixels.
What if you allowed 3 colors or any number of different colors. Is it 3 to the power of however many pixels you work with?
What is the generalization of the formula? Thank you!
Solution 1:[1]
This Question Should Be Posted On The Math Stack-Exchange But Nevertheless Here's How You Solve It.
This Is A Type Of Permutation Problem.
Lets Consider Each Pixel to be a box and the color to be a ball.
First box can store one out of k balls. So No Of Possibilities is k.
Second Box Can Store one out of k balls. So No Of Possibilities is again k.
But No Of Possibilities if both of them take place is k^2
Generalizing It For n Boxes: It Is k^n
Where in your question k is no of color choices and n is no of pixels.
Sources
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Source: Stack Overflow
| Solution | Source |
|---|---|
| Solution 1 | mrtechtroid |