ICG { 39 } 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 { 39 } :

LINE #
for
identification
purposes		 Value
of
'X'		 Number of
Combinations
for 39 things
taken 'X' at a time
--- --- --- --- ---
Line 00 0 1
Line 01 1 39
Line 02 2 741
Line 03 3 9 139
Line 04 4 82 251
Line 05 5 575 757
Line 06 6 3 262 623
Line 07 7 15 380 937
Line 08 8 61 523 748
Line 09 9 211 915 132
Line 10 10 635 745 396
Line 11 11 1 676 056 044
Line 12 12 3 910 797 436
Line 13 13 8 122 425 444
Line 14 14 15 084 504 396
Line 15 15 25 140 840 660
Line 16 16 37 711 260 990
Line 17 17 51 021 117 810
Line 18 18 62 359 143 990
Line 19 19 68 923 264 410
Line 20 20 68 923 264 410
Line 21 21 62 359 143 390
Line 22 22 51 021 117 810
Line 23 23 37 711 260 990
Line 24 24 25 140 840 660
Line 25 25 15 084 504 396
Line 26 26 8 122 425 444
Line 27 27 3 910 797 436
Line 28 28 1 676 056 044
Line 29 29 635 745 396
Line 30 30 211 915 132
Line 31 31 61 523 748
Line 32 32 15 380 937
Line 33 33 3 262 623
Line 34 34 575 757
Line 35 35 82 251
Line 36 36 9 139
Line 37 37 741
Line 38 38 39
Line 39 39 1
GRAND TOTAL 549 755 813 888
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 36		 137 439 215 616
Group ONE 01 05 09 13 17 21
25 29 33 37		 137 438 691 328
Group TWO 02 06 10 14 18 22
26 30 34 38		 137 438 691 328
Group THREE 03 07 11 15 19 23
27 31 35 39		 137 439 215 616
GRAND TOTAL 549 755 813 888
GRAND TOTAL divided by 4 137 438 953 472
Discrepancy 262 144

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Note 1 : { 2^39 } = 549,755,813,888

Note 2 : { 2^18 } = 262,144

Note 3 : [ Discrepancy ] is given by :

minus

go to Combinatorics Table for { 38 }

go to Combinatorics Table for { 40 }

go back to Section 6 before branching here

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original dated 2004-12-18