ICG { 44 } 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 { 44 } :

LINE #
for
identification
purposes		 Value
of
'X'		 Number of
Combinations
for 44 things
taken 'X' at a time
--- --- --- --- ---
Line 00 0 1
Line 01 1 44
Line 02 2 946
Line 03 3 13 244
Line 04 4 135 751
Line 05 5 1 086 008
Line 06 6 7 059 052
Line 07 7 38 320 568
Line 08 8 177 232 627
Line 09 9 708 930 508
Line 10 10 2 481 256 778
Line 11 11 7 669 339 132
Line 12 12 21 090 682 613
Line 13 13 51 915 526 432
Line 14 14 114 955 808 528
Line 15 15 229 911 617 056
Line 16 16 416 714 805 914
Line 17 17 686 353 797 976
Line 18 18 1 029 530 696 964
Line 19 19 1 408 831 480 056
Line 20 20 1 761 039 350 070
Line 21 21 2 012 616 400 080
Line 22 22 2 104 098 963 720
Line 23 23 2 012 616 400 080
Line 24 24 1 761 039 350 070
Line 25 25 1 408 831 480 056
Line 26 26 1 029 530 696 964
Line 27 27 686 353 797 976
Line 28 28 416 714 805 914
Line 29 29 229 911 617 056
Line 30 30 114 955 808 528
Line 31 31 51 915 526 432
Line 32 32 21 090 682 613
Line 33 33 7 669 339 132
Line 34 34 2 481 256 778
Line 35 35 708 930 508
Line 36 36 177 232 627
Line 37 37 38 320 568
Line 38 38 7 059 052
Line 39 39 1 086 008
Line 40 40 135 751
Line 41 41 13 244
Line 42 42 946
Line 43 43 44
Line 44 44 1
GRAND TOTAL divided by 4 4 398 046 511 104
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		 4 398 044 413 952
Group ONE 01 05 09 13 17 21
25 29 33 37 41		 4 398 046 511 104
Group TWO 02 06 10 14 18 22
26 30 34 38 42		 4 398 048 608 256
Group THREE 03 07 11 15 19 23
27 31 35 39 43 47		 4 398 046 511 104
GRAND TOTAL 17 592 186 044 416
GRAND TOTAL divided by 4 4 398 046 511 104
Discrepancy 2 097 152

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Note 1 : { 2^44 } = 17,592,186,044,416

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

Note 3 : [ Discrepancy ] is given by :

minus

go to Combinatorics Table for { 43 }

go to Combinatorics Table for { 45 }

go back to Section 6 before branching here

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original dated 2004-12-18