ICG { 32 } Combinatorics Table

An Approach to the 'I-CHING'

by Frank C. Fung ( 1st published in September, 2004 )

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Combinatorics for the Number { 32 } :

LINE #
for
identification
purposes		 Value
of
'X'		 Number of
Combinations
for 32 things
taken 'X' at a time
--- --- --- --- ---
Line 00 0 1
Line 01 1 32
Line 02 2 496
Line 03 3 4 960
Line 04 4 35 960
Line 05 5 201 376
Line 06 6 906 192
Line 07 7 3 365 856
Line 08 8 10 518 300
Line 09 9 28 048 800
Line 10 10 64 512 240
Line 11 11 129 024 480
Line 12 12 225 792 840
Line 13 13 347 373 600
Line 14 14 471 435 600
Line 15 15 565 722 720
Line 16 16 601 080 390
Line 17 17 565 722 720
Line 18 18 471 435 600
Line 19 19 347 373 600
Line 20 20 225 792 840
Line 21 21 129 024 480
Line 22 22 64 512 240
Line 23 23 28 048 800
Line 24 24 10 518 300
Line 25 25 3 365 856
Line 26 26 906 192
Line 27 27 201 376
Line 28 28 35 960
Line 29 29 4 960
Line 30 30 496
Line 31 31 32
Line 32 32 1
GRAND TOTAL 4 294 967 296
SUMMARY : ( based on { modulo 4 } )
NAME OF
GROUP		 Line I.D.'s of
Lines in the Group		 TOTAL SUM of all
Lines in the Group
Group ZERO 00 04 08 12 16 20
24 28 32		 1 073 774 592
Group ONE 01 05 09 13 17 21
25 29		 1 073 741 824
Group TWO 02 06 10 14 18 22
26 30		 1 073 709 056
Group THREE 03 07 11 15 19 23
27 31		 1 073 741 824
GRAND TOTAL 4 294 967 296
GRAND TOTAL divided by 4 1 073 741 824
Discrepancy 32 768

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Note 1 : { 2^32 } = 4,294,967,296

Note 2 : { 2^15 } = 32,768

Note 3 : [ Discrepancy ] is given by :

minus

go to Combinatorics Table for { 31 }

go to Combinatorics Table for { 33 }

go back to Section 6 before branching here

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original dated 2004-12-18