ICG { 31 } 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 { 31 } :

LINE #
for
identification
purposes		 Value
of
'X'		 Number of
Combinations
for 31 things
taken 'X' at a time
--- --- --- --- ---
Line 00 0 1
Line 01 1 31
Line 02 2 465
Line 03 3 4 495
Line 04 4 31 465
Line 05 5 169 911
Line 06 6 736 281
Line 07 7 2 629 575
Line 08 8 7 888 725
Line 09 9 20 160 075
Line 10 10 44 352 165
Line 11 11 84 672 315
Line 12 12 141 120 525
Line 13 13 206 253 075
Line 14 14 265 182 525
Line 15 15 300 540 195
Line 16 16 300 540 195
Line 17 17 265 182 525
Line 18 18 206 253 075
Line 19 19 141 120 525
Line 20 20 84 672 315
Line 21 21 44 352 165
Line 22 22 20 160 075
Line 23 23 7 888 725
Line 24 24 2 629 575
Line 25 25 736 281
Line 26 26 169 911
Line 27 27 31 465
Line 28 28 4 495
Line 29 29 465
Line 30 30 31
Line 31 31 1
GRAND TOTAL 2 147 483 648
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		 536 887 296
Group ONE 01 05 09 13 17 21
25 29		 536 854 528
Group TWO 02 06 10 14 18 22
26 30		 536 854 528
Group THREE 03 07 11 15 19 23
27 31		 536 887 296
GRAND TOTAL 2 147 483 648
GRAND TOTAL divided by 4 536 870 912
Discrepancy 16 384

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Note 1 : { 2^31 } = 2,147,483,648

Note 2 : { 2^14 } = 16,384

Note 3 : [ Discrepancy ] is given by :

minus

go to Combinatorics Table for { 30 }

go to Combinatorics Table for { 32 }

go back to Section 6 before branching here

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original dated 2004-12-18