ICG { 48 } Combinatorics Table

An Approach to the 'I-CHING'

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

Top Of Page

Combinatorics for the Number { 48 } :

LINE #
for
identification
purposes		 Value
of
'X'		 Number of
Combinations
for 48 things
taken 'X' at a time
--- --- --- --- ---
Line 00 0 1
Line 01 1 48
Line 02 2 1 128
Line 03 3 17 296
Line 04 4 194 580
Line 05 5 1 712 304
Line 06 6 12 271 512
Line 07 7 73 629 072
Line 08 8 377 348 994
Line 09 9 1 677 106 640
Line 10 10 6 540 715 896
Line 11 11 22 595 200 368
Line 12 12 69 668 534 468
Line 13 13 192 928 249 296
Line 14 14 482 320 623 240
Line 15 15 1 093 260 079 344
Line 16 16 2 254 848 913 647
Line 17 17 4 244 421 484 512
Line 18 18 7 309 837 001 104
Line 19 19 11 541 847 896 480
Line 20 20 16 735 679 449 896
Line 21 21 22 314 239 266 528
Line 22 22 27 385 657 281 648
Line 23 23 30 957 699 535 776
Line 24 24 32 247 603 683 100
Line 25 25 30 957 699 535 776
Line 26 26 27 385 657 281 648
Line 27 27 22 314 239 266 528
Line 28 28 16 735 679 449 896
Line 29 29 11 541 847 896 480
Line 30 30 7 309 837 001 104
Line 31 31 4 244 421 484 512
Line 32 32 2 254 848 913 647
Line 33 33 1 093 260 079 344
Line 34 34 482 320 623 240
Line 35 35 192 928 249 296
Line 36 36 69 668 534 468
Line 37 37 22 595 200 368
Line 38 38 6 540 715 896
Line 39 39 1 677 106 640
Line 40 40 377 348 994
Line 41 41 73 629 072
Line 42 42 12 271 512
Line 43 43 1 172 304
Line 44 44 194 580
Line 45 45 17 296
Line 46 46 1 128
Line 47 47 48
Line 48 48 1
GRAND TOTAL 281 474 976 710 656
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		 70 368 752 566 272
Group ONE 01 05 09 13 17 21
25 29 33 37 41 45		 70 368 744 177 664
Group TWO 02 06 10 14 18 22
26 30 34 38 42 46		 70 368 735 789 056
Group THREE 03 07 11 15 19 23
27 31 35 39 43 47		 70 368 744 177 664
GRAND TOTAL 281 474 976 710 656
GRAND TOTAL divided by 4 70 368 744 177 664
Discrepancy 8 388 608

go to Top Of Page

Note 1 : { 2^48 } = 281,474,976,710,656

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

Note 3 : [ Discrepancy ] is given by :

minus

go to Combinatorics Table for { 47 }

go to Combinatorics Table for { 49 }

go back to Seciton 6 before branching here

return to The ICG HomePage

original dated 2004-12-18