ICG { 40 } Combinatorics Table

An Approach to the 'I-CHING'

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

Top Of Page

Combinatorics for the Number { 40 } :

LINE #
for
identification
purposes		 Value
of
'X'		 Number of
Combinations
for 40 things
taken 'X' at a time
--- --- --- --- ---
Line 00 0 1
Line 01 1 40
Line 02 2 780
Line 03 3 9 880
Line 04 4 91 390
Line 05 5 658 008
Line 06 6 3 838 380
Line 07 7 18 643 560
Line 08 8 76 904 685
Line 09 9 273 438 880
Line 10 10 847 660 528
Line 11 11 2 311 801 440
Line 12 12 5 586 853 480
Line 13 13 12 033 222 880
Line 14 14 23 206 929 840
Line 15 15 40 225 345 056
Line 16 16 62 852 101 650
Line 17 17 88 732 378 800
Line 18 18 113 380 261 800
Line 19 19 131 282 408 400
Line 20 20 137 846 528 820
Line 21 21 131 282 408 400
Line 22 22 113 380 261 800
Line 23 23 88 732 378 800
Line 24 24 62 852 101 650
Line 25 25 40 225 345 056
Line 26 26 23 206 929 840
Line 27 27 12 033 222 880
Line 28 28 5 586 853 480
Line 29 29 2 311 801 440
Line 30 30 847 660 528
Line 31 31 273 438 880
Line 32 32 76 904
Line 33 33 18 643 560
Line 34 34 3 838 380
Line 35 35 658 008
Line 36 36 91 390
Line 37 37 9 880
Line 38 38 780
Line 39 39 40
Line 40 40 1
GRAND TOTAL 1 099 511 627 776
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		 274 878 431 232
Group ONE 01 05 09 13 17 21
25 29 33 37		 274 877 906 944
Group TWO 02 06 10 14 18 22
26 30 34 38		 274 877 382 656
Group THREE 03 07 11 15 19 23
27 31 35 39		 274 877 906 944
GRAND TOTAL 1 099 511 627 776
GRAND TOTAL divided by 4 274 877 906 944
Discrepancy 524 288

go to Top Of Page

Note 1 : { 2^40 } = 1,099,511,627,776

Note 2 : { 2^19 } = 524,288

Note 3 : [ Discrepancy ] is given by :

minus

go to Combinatorics Table for { 39 }

go to Combinatorics Table for { 41 }

go back to Section 6 before branching here

return to The ICG HomePage

original dated 2004-12-18