Only Pure Think

Quiz 69: Digital picture
A digital picture has 4x2 pixels sensor. Each pixel can have 256 levels of colors (8 bit).

Well, how many different pictures can be taken?

Go, think and go!

Well, let's divide the sensor in two parts: the left one with 4 pixels and the right one with 4 pixels as well.

1) Now, let's start from the first combination of the left part (for instance all 4 pixels white). In this case, the right part has got 256x256x256x256=256^4 different combinations.

2) Let's take now the second combination of the left part, for instance with 1 pixel that has turned from white to the next color. In this case, the right part will have 256^4-1 possible combinations (the combination with pixels all white cannot be taken becase, turning 180° the sensor, was a combination already considered in 1). Therefore, up to now, we have 256^4+(256^4-1) combinations.

Going on in the same way, there will be:
256^4+(256^4-1)+(256^4-2)+...+2+1=(256^4+1)x256^4/2=1.8x10^19 different combinations and therefore 1.8x10^19 different pictures!!!
Congratulations to Mc

Solution (256^4+1)x256^4/2=1.8x10^19

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