What is the total number of possible Sudoku answer configurations? And can this answer be arrived at analytically using combinatorics, or must it be counted manually using computers?

Well the number is kinda too big to be counted manually accurately. Here is an article about the number of clues needed for a unique Sudoku solution:
http://www.math.ie/McGuire_V1.pdf
Apparently they used computers to check for every 16 clue Sudoku, but they also applied some combinatorics too.

The number of valid Sudoku solution grids for the standard 9×9 grid was calculated by Bertram Felgenhauer and Frazer Jarvis in 2005 to be 6,670,903,752,021,072,936,960.

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TopNewestWell the number is kinda too big to be counted manually accurately. Here is an article about the number of clues needed for a unique Sudoku solution: http://www.math.ie/McGuire_V1.pdf Apparently they used computers to check for every 16 clue Sudoku, but they also applied some combinatorics too.

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The number of valid Sudoku solution grids for the standard 9×9 grid was calculated by Bertram Felgenhauer and Frazer Jarvis in 2005 to be 6,670,903,752,021,072,936,960.

You can refer to their website for further details.

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ha!ha! iam an expert in sudoku

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no no combinations only

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Thanks :)

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I thin it's possible to wwrite the probability as an operation, but you can not count it manually

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The value is too BIG!!!

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