I thought it might be fun to compute the total number of possible movies, based on frame rate, resolution, and the number of possible colors on a standard high-definition digital blu-ray or something. So with some input from people who know more than I do about those things, I came up with the following numbers:
2203 = 10648000 colors/pixel 24 frames/second 1920*1080=2073600 pixels/frameAnd I want to calculate all of the possible movies with runnings times less than or equal to exactly four hours.
(4 hours = 14400 sec) * (24 frames/sec) = 345600 framesBased on the numbers for colors/pixel and pixels/frame, the number of possible frames should be
106480002073600So for any particular number of frames n, we should have exactly
(106480002073600)npossible movies. So for all possible movies less than or equal to four hours, we have to sum up these terms for all n from 0 to 345600. According to the appropriate summation formula, this is equal to exactly
log10(10648000716638233600) = 716638233600(log1010648000) = 5036008956987So we're talking about a number that has over five trillion digits. That's so many movies that if you watched a movie every day for the rest of the month, you still wouldn't be done!