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spelling and format editing has occurred within these posts; some email addresses may be out of date. ------------------------------------------ Subj: number of possible readings Date: Sat, Feb 17, 1996 12:03 AM PDT Mike McCormick (email@example.com) wrote: Glenn Wallace asked: > Would the mathematician here on the list help me to > understand these possibilities? > 1. How many possible combinations/permutations are > there in the whole I Ching system using "no" changing > lines? Answer: 64 > 2. How many possible combinations are there in the whole > I Ching system using 1 changing line? Answer: 64 x 6 = 384 For each of the 64 possible first hexagrams, there are 6 possible second hexagrams if just one line moves. Therefore the total number of such readings is 64 x 6. > 3. How many using 2 changing lines? Answer: 64 x 15 = 960. The reason for this is that there are 15 different ways to get 2 moving lines. This is calculated using the combinatoric "6 choose 2" formula 6!/(6-2)!2! = 15. > 4. How many using 3 changing lines? The correct answer is 64 x 20 = 1280. There are 20 ways to get 3 moving lines, using the formula 6!/(6-3)!3!. > 5. How many using 4 changing lines? The answer is 64 x 15 = 960. There are 15 ways to get 4 moving lines, using the formula 6!/(6-4)!4!. It is not a coincidence that this is the same answer as to question #3; it follows the standard combinatoric bell curve. > 6. How many using 5 changing lines? The answer is 64 x 6 = 384. There are 6 ways to get 5 moving lines. This is per the formula 6!/(6-5)!5! = 6!/5! = 6. But you don't have to know math to figure out this one, just use common sense: To count how many ways to get 5 moving lines, you can just count how many ways there to get the one line that's *not* moving, which is 6. > 7. How many using 6 changing lines ? Answer: Just 64. Forget math, just think about it a moment. Given some initial hexagram, if all 6 lines move then there is only one possible second hexagram. One reading per initial hexagram -> 64 possible first hexagrams -> 64 readings. > 8. How many total possible combinations/permutations in > the whole I Ching system? Answer: 4096. In general, a I Ching reading can begin with any of 64 hexagrams, and move to any of 64 second hexagrams (counting the no moving lines case as "moving" to the same hexagram), therefore the total possible readings is simply 64 x 64 = 4096. Just as a sanity check, note that the seven previous answers I gave do total 4096: 4096 = 64 + 384 + 960 + 1280 + 960 + 384 + 64. An interesting aside about the magic I Ching number 4096: In the octal notation that computer programmers and mathematicians use, 4096 is written as 10000, and in the I Ching the totality of everything in the world is often called "the ten thousand things". Hope this helps... Mike McCormick firstname.lastname@example.org
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