Simple combinatorics gone wrong

In summary, this person is trying to figure out how many photos they can take with an 8 megapixel camera resolution with 3264x2448 pixels. They are trying to find a solution using equations and they are sure the answer is 17 million. They also mention a format for the photos, jpeg.
  • #1
x2thay
14
0
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.




Homework 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.
 
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  • #2
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.
 
Last edited:
  • #3
x2thay said:
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.




Homework 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?
 
  • #4
jedishrfu said:
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.
 
  • #5
Dick said:
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.
 
  • #6
x2thay said:
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).
 
  • #7
x2thay said:
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.
 
  • #8
rollingstein said:
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.
 
  • #9
Okay, got it. The solution is a number whose log is 115 805 766.
Thanks, guys.
 

What is "Simple combinatorics gone wrong"?

"Simple combinatorics gone wrong" refers to the concept of using basic combinatorial principles to solve a problem, but making a mistake in the process that leads to an incorrect solution.

What are some common mistakes in simple combinatorics?

Some common mistakes in simple combinatorics include miscounting, double counting, and not considering all possible combinations.

How can we avoid making mistakes in simple combinatorics?

To avoid making mistakes in simple combinatorics, it is important to carefully consider all possible combinations and to double check our calculations. It can also be helpful to break down the problem into smaller, more manageable parts.

What are some real-life examples of simple combinatorics gone wrong?

One example of simple combinatorics gone wrong is the Monty Hall problem, where people often make the mistake of assuming that switching doors does not change their chances of winning. Another example is the birthday problem, where people often underestimate the number of people needed in a room for there to be a high chance of two people sharing the same birthday.

How can understanding simple combinatorics help us in our daily lives?

Understanding simple combinatorics can help us in our daily lives by allowing us to make more informed decisions and solve problems more efficiently. For example, understanding basic probability can help us make better financial decisions or analyze data more accurately.

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