01 November 2009

Sudoku Math

I enjoy puzzles. I always have. Crosswords, logic puzzles, cryptograms, and number puzzles. That said, the Japanese "sudoku" puzzle is actually a fairly recent source of enjoyment for me. I never learned about them when growing up, and only did my first one while I was still in college.

So today, while I was working on a sudoku puzzle, I started to wonder how many different combinations of those 81 digits there could possibly be. Now, I'm no mathematician, but others are, and a quick Google search gave me my answer: there are 6,670,903,752,021,072,936,960 possible LEGAL sudoku number puzzle combinations.

Or in word form: six sextillion, six hundred seventy quintillion, nine hundred three quadrillion, seven hundred fifty-two trillion, twenty-one billion, seventy-two million, nine hundred thirty-six thousand, nine hundred sixty. That is (really roughly) 6.67 x 10^21 puzzles. That's about three times more puzzle combinations than there are atoms in a standard U.S. penny. It's also about 300 times more puzzles than there are red blood cells in the adult human body. And it's about 8,130,000,000 times the amount of U.S. dollars in circulation around the world as of 2007.

A guy by the name of Bertram Felgenhauer and his partner Frazer Jarvis came up with the calculation for this number back in 2005: (2^15)(3^8)(5^7)(27,204,267,971) = (9!)(72^2)(2^7)(27,204,267,971) = 6.67*10^21 puzzles.

However, the number of essentially different puzzles, meaning puzzles which aren't so close to being alike that all you'd have to do is swap a couple numbers and it's pretty much the same for everything else was calculated to be a mere 5,472,730,538 puzzles by Mr. Jarvis and his partner Ed Russell.

Why am I posting this information? Didn't I know it would make most people have a headache by the time they finished reading? Yes. Absolutely. I just found it interesting and wanted to write. So there. Point of the post: go do a sudoku puzzle with this new perspective on just how many combinations there could possibly be to fit those numbers into there. It'll blow your mind (again)!

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