ICG { 37 } 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 { 37 } :

LINE #
for
identification
purposes		 Value
of
'X'		 Number of
Combinations
for 37 things
taken 'X' at a time
--- --- --- --- ---
Line 00 0 1
Line 01 1 37
Line 02 2 666
Line 03 3 7 770
Line 04 4 66 045
Line 05 5 435 897
Line 06 6 2 324 784
Line 07 7 10 295 472
Line 08 8 38 608 020
Line 09 9 124 403 620
Line 10 10 348 330 136
Line 11 11 854 992 152
Line 12 12 1 852 482 996
Line 13 13 3 562 467 300
Line 14 14 6 107 086 800
Line 15 15 9 364 199 760
Line 16 16 12 875 774 670
Line 17 17 15 905 368 710
Line 18 18 17 672 631 900
Line 19 19 17 672 631 900
Line 20 20 15 905 368 710
Line 21 21 12 875 774 670
Line 22 22 9 364 199 760
Line 23 23 6 107 086 800
Line 24 24 3 562 467 300
Line 25 25 1 852 482 996
Line 26 26 854 992 152
Line 27 27 348 330 136
Line 28 28 124 403 620
Line 29 29 38 608 020
Line 30 30 10 295 472
Line 31 31 2 324 784
Line 32 32 435 897
Line 33 33 66 045
Line 34 34 7 770
Line 35 35 666
Line 36 36 37
Line 37 37 1
GRAND TOTAL 137 438 953 472
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		 34 359 607 296
Group ONE 01 05 09 13 17 21
25 29 33 37		 34 359 607 296
Group TWO 02 06 10 14 18 22
26 30 34		 34 359 869 440
Group THREE 03 07 11 15 19 23
27 31 35		 34 359 869 440
GRAND TOTAL 137 438 953 472
GRAND TOTAL divided by 4 137 438 953 472
Discrepancy 131 072

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Note 1 : { 2^37 } = 137,438,953,472

Note 2 : { 2^17 } = 131,072

Note 3 : [ Discrepany ] is given by :

minus

go to Combinatorics Table for { 36 }

go to Combinatorics Table for { 38 }

go back to Section 6 before branching here

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original dated 2004-12-18