# Simple combinatorics gone wrong...

by x2thay
Tags: combinatorics, simple
 P: 14 1. So consider an 8 megapixel picture (res: 3264x2448). Now, it seems rather simple but I just can't figure out how to calculate the entire number of possible shots/photographs one can take within that resolution, assuming each pixel can have 16777216 different values/colors. 2. Relevant equations 3. The attempt at a solution So I realize the number has to be absolutely monstruous, so here's what I've tried so far (3264*2448)!*2^24 Meaning, the entire possible positions all the pixels can assume times all the different values each individual pixel can have.
 P: 2,201 It seems your solution is correct for a JPG image but for a GIF you limited to 256 colors per image. Each color may range from 0 to 16million as a GIF uses an 8 bit value that indicates which color register from the color palette to use. One problem I see is that you'll get shots all in one color or half one color half another... Do you want to define what a photo is? like it must have a minimum of X colors per photo? Next what about color changes that are imperceptibly small? Do you want to instead say that while RED can range from 0 to 255 in value we'll limit it down to a subset of {0, 16, 32, 48, 64 ... 255} in other words 64 color choices.
HW Helper
Thanks
P: 24,460
 Quote by x2thay 1. So consider an 8 megapixel picture (res: 3264x2448). Now, it seems rather simple but I just can't figure out how to calculate the entire number of possible shots/photographs one can take within that resolution, assuming each pixel can have 16777216 different values/colors. 2. Relevant equations 3. The attempt at a solution So I realize the number has to be absolutely monstruous, so here's what I've tried so far (3264*2448)!*2^24 Meaning, the entire possible positions all the pixels can assume times all the different values each individual pixel can have.
If you have 2^24 possible values of each pixel, then for two pixels you would have 2^24*2^24 possibilities, right? What about 3264*2448 pixels?

P: 14

## Simple combinatorics gone wrong...

 Quote by jedishrfu It seems your solution is correct for a JPG image but for a GIF you limited to 256 colors per image. Each color may range from 0 to 16million as a GIF uses an 8 bit value that indicates which color register from the color palette to use. One problem I see is that you'll get shots all in one color or half one color half another... Do you want to define what a photo is? like it must have a minimum of X colors per photo? Next what about color changes that are imperceptibly small? Do you want to instead say that while RED can range from 0 to 255 in value we'll limit it down to a subset of {0, 16, 32, 48, 64 ... 255} in other words 64 color choices.
No matter how insignificant the difference is, I meant to calculate e-v-e-r-y single possible matrix 3264x2448 arrangement, given that each entry can assume 2^24 different values. so yes, there will be an enormous amount of shots in which the only difference from the next, will be a single pixel.
P: 14
 Quote by Dick If you have 2^24 possible values of each pixel, then for two pixels you would have 2^24*2^24 possibilities, right? What about 3264*2448 pixels?
So... (2^24)^(3264*2448) ? Basically 17M^8M? Are you sure that's correct? It seems too simple.
HW Helper
Thanks
P: 24,460
 Quote by x2thay So... (2^24)^(3264*2448) ? Basically 17M^8M? Are you sure that's correct? It seems too simple.
Yes, I'm sure. It's actually too simple for me to be wrong. It's (number of possibilities for each choice)^(number of choices).
P: 301
 Quote by x2thay So... (2^24)^(3264*2448) ? Basically 17M^8M? Are you sure that's correct? It seems too simple.
What format? You didn't answer.

Since jpeg is a lossy format a lot of those combinations ought to evaluate to the same output. I could be wrong.
P: 14
 Quote by rollingstein What format? You didn't answer. Since jpeg is a lossy format a lot of those combinations ought to evaluate to the same output. I could be wrong.
I should have mentioned earlier, but I meant a bitmap format.
 P: 14 Okay, got it. The solution is a number whose log is 115 805 766. Thanks, guys.

 Related Discussions General Math 7 Set Theory, Logic, Probability, Statistics 3 General Math 4 General Math 5 Set Theory, Logic, Probability, Statistics 5