ICG { 49 } Combinatorics Tables

An Approach to the 'I-CHING'

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

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Combinatorics for the Number { 49 } :

LINE #
for
identicifcation
purposes		 Value
of
'X'		 Number of
Combinations
for 49 things
taken 'X' at a time
--- --- --- --- ---
Line 00 0 1
Line 01 1 49
Line 02 2 1 176
Line 03 3 18 424
Line 04 4 211 876
Line 05 5 1 906 884
Line 06 6 13 983 816
Line 07 7 85 900 584
Line 08 8 450 978 066
Line 09 9 2 054 455 634
Line 10 10 8 217 822 536
Line 11 11 29 135 916 264
Line 12 12 92 263 734 836
Line 13 13 262 596 783 764
Line 14 14 675 248 872 536
Line 15 15 1 575 580 702 584
Line 16 16 3 348 108 992 991
Line 17 17 6 499 270 398 159
Line 18 18 11 554 258 485 616
Line 19 19 18 851 684 897 584
Line 20 20 28 277 527 346 376
Line 21 21 39 049 918 716 424
Line 22 22 49 699 896 548 176
Line 23 23 58 343 356 817 424
Line 24 24 63 205 303 218 876
Line 25 25 63 205 303 218 876
Line 26 26 58 343 356 817 424
Line 27 27 49 699 896 548 176
Line 28 28 39 049 918 716 424
Line 29 29 28 277 527 346 376
Line 30 30 18 851 684 897 584
Line 31 31 11 554 258 485 616
Line 32 32 6 499 270 398 159
Line 33 33 3 348 108 992 991
Line 34 34 1 575 580 702 584
Line 35 35 675 248 872 536
Line 36 36 262 596 783 764
Line 37 37 92 263 734 836
Line 38 38 29 135 916 264
Line 39 39 8 217 822 536
Line 40 40 2 054 455 634
Line 41 41 450 978 066
Line 42 42 85 900 584
Line 43 43 13 983 816
Line 44 44 1 906 884
Line 45 45 211 876
Line 46 46 18 424
Line 47 47 1 176
Line 48 48 49
Line 49 49 1
GRAND TOTAL 562 949 953 421 312
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 48		 140 737 496 743 936
Group ONE 01 05 09 13 17 21
25 29 33 37 41 45 49		 140 737 496 743 936
Group TWO 02 06 10 14 18 22
26 30 34 38 42 46		 140 737 479 966 720
Group THREE 03 07 11 15 19 23
27 31 35 39 43 47		 140 737 479 966 720
GRAND TOTAL 562 949 953 421 312
GRAND TOTAL divided by 4 140 737 488 355 328
Discrepancy 8 388 608

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Note 1 : { 2^49 } = 562,949,953,421,312

Note 2 : { 2^23 } = 8,388,608

Note 3 : [ Discrepancy ] is given by :

minus

go to Combinatorics Table for { 48 }

go back to Section 6 before branching here

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original dated 2004-12-18