As per request, I’m starting a thread on the total number of Liu Yao combinations.
Due to some confusion regarding my post about the total number of Ba Zi permutations, I’ll be offering a variety of different calculations.
If there are other tallies that I miss, please add them to the thread.
First things first: the total number of castable hexagrams
This part is easy, thank goodness!
We have 64 hexagrams. Each hexagram can have changing lines which change it into one of the other 63 hexagrams.
64x63=4,032 possible physical castings.
Now, as for including the date of casting... well, that depends on how many pillars a person is using, as well as whether or not they are taking the “hidden stem Branch flavors” Into account!
Let’s start with the traditional, flavorless date layout of month pillar + day pillar:
60 months x 60 days = 3,600
So we have 3,600 different dates where we can cast 4,032 different hexagrams...
3,600 x 4,032 = 14,515,200 different casting scenarios!
Now, I’ve seen some references to schools including the (still flavorless) year pillar.
In that case, 60 years x 12 months x 60 days = 43,200 different casting dates.
43,200 x 4,032 = 174,182,400 different casting scenarios!
I have ALSO seen references to schools excluding the year pillar but including The hour pillar.
Since there are two schools of thought on how many hour pillars are in a day (12 or 13), let’s do the math for both:
12 hours x 60 days x 60 months = 43,200
43,200 x 4,032 = 174,182,400 different casting scenarios
13 hours x 60 days x 60 months = 46,800
46,800 x 4,032 = 188,697,600 different casting scenarios
Lastly, some people use all 4 pillars, and again we’ll have two different results based on how the hour pillar is being laid out (12 or 13 hours):
60 years x 12 months x 60 days x 12 hours = 518,400
518,400 x 4,032 = 2,090,188,800 different casting scenarios
60 years x 12 months x 60 days x 13 hours = 561,600
561,600 x 4,032 = 2,264,371,200 different casting scenarios.
Now, I’m going to add “flavor”. This means I’m going to calculate the scenarios based on which hidden stem is dominant in any given branch, which is dependent on exactly where in a branch’s cycle the casting occurs.
Starting with just the month & day branch, we must do some tedious, repetitious calculations:
60 month branch 气 times x 60 day Branch 气 times = 3,600
60 month branch 气 times x 60 day branch early 节 times = 3,600;
60 month branch 气 times x 35 day branch mid 节 times = 2,100;
60 month branch early 节 times x 60 day branch 气 times = 3,600;
60 month branch early 节 times x 60 day branch early 节 times = 3,600;
60 month branch early 节 times x 35 day branch mid 节 times = 2,100;
35 month branch mid 节 times x 60 day branch 气 times = 2,100;
35 month branch mid 节 times x 60 day branch early 节 times = 2,100;
35 month branch mid 节 times x 35 day branch mid 节 times = 1,125;
Total number of different casting dates: 23,925
23,925 x 4,032 = 96,465,600 different “flavored” casting scenarios!
Taking into account all 4 “flavored” pillars (13 hour pillars), we’d get:
2,264,125 x 4,032 = 9,128,952,000 “flavored” casting scenarios!
So, even with just the traditional, “flavorless” day & month pillars, we get over 14.5 million different casting scenarios... and additional “flavorless” pillars can drive the number of possibilities up to over 2.2 BILLION different casting scenarios.
“Flavored” day & month pillars give us almost 96.5 million different casting scenarios, and additional “flavored” pillars can drive up the number of possibilities to over 9 BILLION different casting scenarios.
*note: my use of “节” & “气” labels outside of the month pillar is simply to identify the beginning, middle & end of a branch cycle, regardless of which pillar it is in.
