ICG { 45 } 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 { 45 } :

LINE #
for
identification
purposes		 Value
of
'X'		 Number of
Combinations
for 45 things
taken 'X' at a time
--- --- --- --- ---
Line 00 0 1
Line 01 1 45
Line 02 2 990
Line 03 3 14 190
Line 04 4 148 995
Line 05 5 1 221 759
Line 06 6 8 145 060
Line 07 7 45 379 620
Line 08 8 215 553 195
Line 09 9 886 163 135
Line 10 10 3 190 187 286
Line 11 11 10 150 595 910
Line 12 12 28 760 021 745
Line 13 13 73 006 209 045
Line 14 14 166 871 334 960
Line 15 15 344 867 425 584
Line 16 16 646 626 422 970
Line 17 17 1 103 068 603 890
Line 18 18 1 715 884 494 940
Line 19 19 2 438 362 177 020
Line 20 20 3 169 870 830 126
Line 21 21 3 773 655 750 150
Line 22 22 4 116 715 363 800
Line 23 23 4 116 715 363 800
Line 24 24 3 773 655 750 150
Line 25 25 3 169 870 830 126
Line 26 26 2 438 362 177 020
Line 27 27 1 715 884 494 940
Line 28 28 1 103 068 603 890
Line 29 29 646 626 422 970
Line 30 30 344 867 425 584
Line 31 31 166 871 334 960
Line 32 32 73 006 209 045
Line 33 33 28 760 021 745
Line 34 34 10 150 595 910
Line 35 35 3 190 187 286
Line 36 36 886 163 135
Line 37 37 215 553 195
Line 38 38 45 379 620
Line 39 39 8 145 060
Line 40 40 1 221 759
Line 41 41 148 995
Line 42 42 14 190
Line 43 43 990
Line 44 44 45
Line 45 45 1
GRAND TOTAL 35 184 372 088 832
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 40 44		 8 796 090 925 056
Group ONE 01 05 09 13 17 21
25 29 33 37 41 45		 8 796 090 925 056
Group TWO 02 06 10 14 18 22
26 30 34 38 42		 8 796 095 119 360
Group THREE 03 07 11 15 19 23
27 31 35 39 43		 8 796 095 119 360
GRAND TOTAL 35 184 372 088 832
GRAND TOTAL divided by 4 8 796 093 022 208
Discrepancy 2 097 152

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Note 1 : { 2^45 } = 35,184,372,088,832

Note 2 : { 2^21 } = 2,097,152

Note 3 : [ Discrepancy ] is given by :

minus

go to Combinatorics Table for { 44 }

go to Combinatorics Table for { 46 }

go back to Section 6 before branching here

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original dated 2004-12-18